Introduction to SHM - Download as Excel by kmb15358

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									                                                            SIMPLE HARMONIC MOTION
A particle oscillates left and right as shown in the diagram below. The y axis is used as the artificial axis for time.
Move the slider to change the angle. Watch what happens on the unit circle.        The angle is to be measured in radians.
                                                                                   as it represents time, a number.
                             0.0628            1    0.06     radians


                                  7



                                  6                                                  3            degrees
                                                                                    0.06          radians

                                  5                                                        1.5



                                  4


                                                                                           0.5
                                  3



                                  2                                 -1.5            -0.5               0.5

                                                                                           -0.5

                                  1



                                  0                                                        -1.5
           -1.5     -1     -0.5       0   0.5      1      1.5
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 ed as the artificial axis for time.
The angle is to be measured in radians. Things to think about::
 s it represents time, a number.
                                        What trigonometric function can represent
                                        the oscillation?

                                        Write down the function.

                                        How would the function change if the particle      t    x1      y1    x1
                                        oscillated twice as fast?                                a      c     a
                                                                                                 1      1     1
                                        How would the function change if it oscillated    Time increment
                                        twice as wide?                                    0.1 Try 0.1               From centre
                                                                                           0     0      1      1        0   0
                                        What is the centre of oscillation?                0.1 0.1       1      1        1 0.1
                                        The collapsed time axis?                          0.2 0.2 0.98         1    cos bit
                                                                                          0.3 0.3 0.96         1        1   0
                                        This motion assumes that the oscillation starts   0.4 0.39 0.92       0.9       0   0
                                        at maximum displacement.                          0.5 0.48 0.88       0.9
                                        What adjustment is needed to the function if it   0.6 0.56 0.83       0.8   trig graph
                                        started elsewhere?                                0.7 0.64 0.76       0.8   y      x
                  0.5             1.5
                                                                                          0.8 0.72 0.7        0.7    0.06      0
                                        Write down the general equation to represent      0.9 0.78 0.62       0.6    0.06      1
                                        simple harmonic motion.                            1 0.84 0.54        0.5
                                                                                          1.1 0.89 0.45       0.5
                                                                                          1.2 0.93 0.36       0.4
                                                                                          1.3 0.96 0.27       0.3
                                        y = Acos(nt + e)                                  1.4 0.99 0.17       0.2
                                        where A is the amplitude, the period is 2p/n      1.5    1     0.07   0.1
                                        and the phase shift is e.                         1.6    1    -0.03   -0
                                                                                          1.7 0.99 -0.13      -0
                                                                                          1.8 0.97 -0.23      -0
                                                                                          1.9 0.95 -0.32      -0
                                                                                           2 0.91 -0.42       -0
                                                                                          2.1 0.86 -0.5       -1
                                                                                          2.2 0.81 -0.59      -1
                                                                                          2.3 0.75 -0.67      -1
                                                                                          2.4 0.68 -0.74      -1
                                                                                          2.5 0.6      -0.8   -1
                                                                                          2.6 0.52 -0.86      -1
                                                                                          2.7 0.43 -0.9       -1
                                                                                          2.8 0.33 -0.94      -1
                                                                                          2.9 0.24 -0.97      -1
                                                                                           3 0.14 -0.99       -1
                                                                                          3.1 0.04      -1    -1
                                                                                          3.2 -0.06 -1        -1
                                                                                          3.3 -0.16 -0.99     -1
                                                                                          3.4 -0.26 -0.97     -1
                                                                                          3.5 -0.35 -0.94     -1
                                                                                          3.6 -0.44 -0.9      -1
                                                                                          3.7 -0.53 -0.85     -1
                                                                                          3.8 -0.61 -0.79     -1
                                                                                          3.9 -0.69 -0.73     -1
                                                                                           4 -0.76 -0.65      -1
4.1   -0.82   -0.57   -1
4.2   -0.87   -0.49   -0
4.3   -0.92    -0.4   -0
4.4   -0.95   -0.31   -0
4.5   -0.98   -0.21   -0
4.6   -0.99   -0.11   -0
4.7     -1    -0.01   -0
4.8     -1     0.09   0.1
4.9   -0.98    0.19   0.2
 5    -0.96    0.28   0.3
5.1   -0.93    0.38   0.4
5.2   -0.88    0.47   0.5
5.3   -0.83    0.55   0.6
5.4   -0.77    0.63   0.6
5.5   -0.71    0.71   0.7
5.6   -0.63    0.78   0.8
5.7   -0.55    0.83   0.8
5.8   -0.46    0.89   0.9
5.9   -0.37    0.93   0.9
 6    -0.28    0.96    1
6.1   -0.18    0.98    1
6.2   -0.08     1      1
6.3    0.02     1      1
6.4    0.12    0.99    1
6.5    0.22    0.98    1
6.6    0.31    0.95    1
6.7    0.4     0.91   0.9
6.8    0.49    0.87   0.9
6.9    0.58    0.82   0.8
 7     0.66    0.75   0.8
7.1    0.73    0.68   0.7
7.2    0.79    0.61   0.6
7.3    0.85    0.53   0.5
7.4    0.9     0.44   0.4
7.5    0.94    0.35   0.3
7.6    0.97    0.25   0.3
7.7    0.99    0.15   0.2
7.8     1      0.05   0.1
7.9     1     -0.05   -0
 8     0.99   -0.15   -0
8.1    0.97   -0.24   -0
8.2    0.94   -0.34   -0
8.3    0.9    -0.43   -0
8.4    0.85   -0.52   -1
8.5    0.8     -0.6   -1
8.6    0.73   -0.68   -1
8.7    0.66   -0.75   -1
8.8    0.58   -0.81   -1
8.9    0.5    -0.87   -1
 9     0.41   -0.91   -1
9.1    0.32   -0.95   -1
9.2    0.22   -0.97   -1
9.3    0.12   -0.99   -1
9.4    0.02     -1    -1
9.5   -0.08     -1    -1
9.6   -0.17   -0.98   -1
9.7   -0.27   -0.96   -1
9.8   -0.37   -0.93   -1
9.9   -0.46   -0.89   -1
10    -0.54   -0.84   -1
10    -0.63   -0.78   -1
10     -0.7   -0.71   -1
10    -0.77   -0.64   -1
10    -0.83   -0.56   -1
11    -0.88   -0.48   -0
11    -0.92   -0.39   -0
11    -0.96   -0.29   -0
11    -0.98   -0.19   -0
11      -1     -0.1   -0
11      -1       0     0
11    -0.99     0.1   0.1
11    -0.98     0.2   0.2
11    -0.95     0.3   0.3
11    -0.92    0.39   0.4
12    -0.88    0.48   0.5
12    -0.82    0.57   0.6
12    -0.76    0.65   0.6
12    -0.69    0.72   0.7
12    -0.62    0.79   0.8
12    -0.54    0.84   0.8
12    -0.45    0.89   0.9
12    -0.36    0.93   0.9
12    -0.26    0.96    1
12    -0.17    0.99    1
13    -0.07      1     1
13     0.03      1     1
13     0.13    0.99    1
13     0.23    0.97    1
13     0.33    0.94   0.9
13     0.42    0.91   0.9
13     0.51    0.86   0.9
13     0.59    0.81   0.8
13     0.67    0.74   0.7
13     0.74    0.67   0.7
14      0.8    0.59   0.6
14     0.86    0.51   0.5
14     0.91    0.42   0.4
14     0.94    0.33   0.3
14     0.97    0.23   0.2
14     0.99    0.14   0.1
14       1     0.04    0
14       1    -0.06   -0
14     0.99   -0.16   -0
14     0.97   -0.26   -0
15     0.93   -0.35   -0
15     0.89   -0.45   -0
15     0.85   -0.53   -1
15     0.79   -0.62   -1
15     0.72   -0.69   -1
15     0.65   -0.76   -1
15     0.57   -0.82   -1
15     0.49   -0.87   -1
15     0.4   -0.92   -1
15     0.3   -0.95   -1
16    0.21   -0.98   -1
16    0.11   -0.99   -1
16    0.01     -1    -1
16   -0.09     -1    -1
16   -0.19   -0.98   -1
16   -0.29   -0.96   -1
16   -0.38   -0.92   -1
16   -0.47   -0.88   -1
16   -0.56   -0.83   -1
16   -0.64   -0.77   -1
17   -0.71    -0.7   -1
17   -0.78   -0.63   -1
17   -0.84   -0.55   -1
17   -0.89   -0.46   -0
17   -0.93   -0.37   -0
17   -0.96   -0.28   -0
17   -0.98   -0.18   -0
17     -1    -0.08   -0
17     -1     0.02    0
17   -0.99    0.12   0.1
18   -0.98    0.22   0.2
18   -0.95    0.32   0.3
18   -0.91    0.41   0.4
18   -0.87     0.5   0.5
18   -0.81    0.58   0.6
18   -0.75    0.66   0.7
18   -0.68    0.73   0.7
18    -0.6     0.8   0.8
18   -0.52    0.85   0.9
18   -0.43     0.9   0.9
19   -0.34    0.94   0.9
19   -0.25    0.97    1
19   -0.15    0.99    1
19   -0.05      1     1
19    0.05      1     1
19    0.15    0.99    1
19    0.25    0.97    1
19    0.34    0.94   0.9
19    0.44     0.9   0.9
19    0.52    0.85   0.9
20    0.61     0.8   0.8
20    0.68    0.73   0.7
20    0.75    0.66   0.7
20    0.81    0.58   0.6
20    0.87     0.5   0.5
20    0.91    0.41   0.4
20    0.95    0.31   0.3
20    0.98    0.22   0.2
20    0.99    0.12   0.1
20      1     0.02    0
21      1    -0.08   -0
21    0.98   -0.18   -0
21    0.96   -0.28   -0
21    0.93   -0.37   -0
21    0.89   -0.46   -0
21    0.84   -0.55   -1
21    0.78   -0.63   -1
21    0.71    -0.7   -1
21    0.64   -0.77   -1
21    0.56   -0.83   -1
22    0.47   -0.88   -1
22    0.38   -0.92   -1
22    0.29   -0.96   -1
22    0.19   -0.98   -1
22    0.09     -1    -1
22   -0.01     -1    -1
22   -0.11   -0.99   -1
22   -0.21   -0.98   -1
22    -0.3   -0.95   -1
22    -0.4   -0.92   -1
23   -0.49   -0.87   -1
23   -0.57   -0.82   -1
23   -0.65   -0.76   -1
23   -0.72   -0.69   -1
23   -0.79   -0.61   -1
23   -0.85   -0.53   -1
23    -0.9   -0.45   -0
23   -0.94   -0.35   -0
23   -0.97   -0.26   -0
23   -0.99   -0.16   -0
24     -1    -0.06   -0
24     -1     0.04    0
24   -0.99    0.14   0.1
24   -0.97    0.24   0.2
24   -0.94    0.33   0.3
24   -0.91    0.42   0.4
24   -0.86    0.51   0.5
24    -0.8     0.6   0.6
24   -0.74    0.67   0.7
24   -0.67    0.74   0.7
25   -0.59    0.81   0.8
25   -0.51    0.86   0.9
25   -0.42    0.91   0.9
25   -0.33    0.95   0.9
25   -0.23    0.97    1
25   -0.13    0.99    1
25   -0.03      1     1
25    0.07      1     1
25    0.17    0.99    1
25    0.26    0.96    1
26    0.36    0.93   0.9
26    0.45    0.89   0.9
26    0.54    0.84   0.8
26    0.62    0.79   0.8
26    0.69    0.72   0.7
26    0.76    0.65   0.6
26    0.82    0.57   0.6
26    0.88    0.48   0.5
26    0.92    0.39   0.4
26    0.95     0.3   0.3
27    0.98     0.2   0.2
27    0.99     0.1   0.1
27      1       0     0
27      1     -0.1   -0
27    0.98    -0.2   -0
27    0.96   -0.29   -0
27    0.92   -0.39   -0
27    0.88   -0.48   -0
27    0.83   -0.56   -1
27    0.77   -0.64   -1
28     0.7   -0.71   -1
28    0.62   -0.78   -1
28    0.54   -0.84   -1
28    0.46   -0.89   -1
28    0.37   -0.93   -1
28    0.27   -0.96   -1
28    0.17   -0.98   -1
28    0.07     -1    -1
28   -0.03     -1    -1
28   -0.13   -0.99   -1
29   -0.22   -0.97   -1
29   -0.32   -0.95   -1
29   -0.41   -0.91   -1
29    -0.5   -0.86   -1
29   -0.59   -0.81   -1
29   -0.66   -0.75   -1
29   -0.73   -0.68   -1
29    -0.8    -0.6   -1
29   -0.86   -0.52   -1
29    -0.9   -0.43   -0
30   -0.94   -0.34   -0
30   -0.97   -0.24   -0
30   -0.99   -0.14   -0
30     -1    -0.05   -0
30     -1     0.05   0.1
30   -0.99    0.15   0.2
30   -0.97    0.25   0.3
30   -0.94    0.35   0.3
30    -0.9    0.44   0.4
30   -0.85    0.53   0.5
31   -0.79    0.61   0.6
31   -0.73    0.69   0.7
31   -0.66    0.75   0.8
31   -0.58    0.82   0.8
31   -0.49    0.87   0.9
31    -0.4    0.91   0.9
31   -0.31    0.95    1
31   -0.21    0.98    1
31   -0.12    0.99    1
31   -0.02      1     1
32    0.08      1     1
32    0.18    0.98    1
32    0.28    0.96    1
32    0.37    0.93   0.9
32    0.47    0.89   0.9
32    0.55    0.83   0.8
32    0.63    0.78   0.8
32    0.71    0.71   0.7
32    0.77    0.63   0.6
32    0.83    0.55   0.6
33    0.88    0.47   0.5
33    0.93    0.38   0.4
33    0.96    0.28   0.3
33    0.98    0.19   0.2
33     1      0.09   0.1
33     1     -0.01   -0
33    0.99   -0.11   -0
33    0.98   -0.21   -0
33    0.95   -0.31   -0
33    0.92    -0.4   -0
34    0.87   -0.49   -0
34    0.82   -0.58   -1
34    0.76   -0.65   -1
34    0.69   -0.73   -1
34    0.61   -0.79   -1
34    0.53   -0.85   -1
34    0.44    -0.9   -1
34    0.35   -0.94   -1
34    0.25   -0.97   -1
34    0.16   -0.99   -1
35    0.06     -1    -1
35   -0.04     -1    -1
35   -0.14   -0.99   -1
35   -0.24   -0.97   -1
35   -0.34   -0.94   -1
35   -0.43    -0.9   -1
35   -0.52   -0.86   -1
35    -0.6    -0.8   -1
35   -0.68   -0.74   -1
35   -0.75   -0.67   -1
36   -0.81   -0.59   -1
36   -0.86    -0.5   -1
36   -0.91   -0.42   -0
36   -0.95   -0.32   -0
36   -0.97   -0.23   -0
36   -0.99   -0.13   -0
36     -1    -0.03   -0
36     -1     0.07   0.1
36   -0.99    0.17   0.2
36   -0.96    0.27   0.3
37   -0.93    0.36   0.4
37   -0.89    0.45   0.5
37   -0.84    0.54   0.5
37   -0.78    0.62   0.6
37   -0.72     0.7   0.7
37   -0.64    0.77   0.8
37   -0.56    0.83   0.8
37   -0.48    0.88   0.9
37   -0.39    0.92   0.9
37   -0.29    0.96    1
38    -0.2    0.98    1
38    -0.1      1     1
38      0       1     1
38     0.1    0.99    1
38     0.2    0.98    1
38     0.3    0.96    1
38    0.39    0.92   0.9
38    0.48    0.88   0.9
38    0.57    0.82   0.8
38    0.64    0.76   0.8
39    0.72     0.7   0.7
39    0.78    0.62   0.6
39    0.84    0.54   0.5
39    0.89    0.45   0.5
39    0.93    0.36   0.4
39    0.96    0.27   0.3
39    0.99    0.17   0.2
39      1     0.07   0.1
39      1    -0.03   -0
39    0.99   -0.13   -0
40    0.97   -0.23   -0
40    0.95   -0.32   -0
40    0.91   -0.42   -0
40    0.86   -0.51   -1
40    0.81   -0.59   -1
40    0.75   -0.67   -1
40    0.67   -0.74   -1
40     0.6    -0.8   -1
40    0.51   -0.86   -1
40    0.43    -0.9   -1
41    0.33   -0.94   -1
41    0.24   -0.97   -1
41    0.14   -0.99   -1
41    0.04     -1    -1
41   -0.06     -1    -1
41   -0.16   -0.99   -1
41   -0.26   -0.97   -1
41   -0.35   -0.94   -1
41   -0.44    -0.9   -1
41   -0.53   -0.85   -1
42   -0.61   -0.79   -1
42   -0.69   -0.73   -1
42   -0.76   -0.65   -1
42   -0.82   -0.57   -1
42   -0.87   -0.49   -0
42   -0.92    -0.4   -0
42   -0.95   -0.31   -0
42   -0.98   -0.21   -0
42   -0.99   -0.11   -0
42     -1    -0.01   -0
43     -1     0.09   0.1
43   -0.98    0.19   0.2
43   -0.96    0.28   0.3
43   -0.93    0.38   0.4
43   -0.88    0.47   0.5
43   -0.83    0.56   0.6
43   -0.77    0.64   0.6
43    -0.7    0.71   0.7
43   -0.63    0.78   0.8
43   -0.55    0.84   0.8
44   -0.46    0.89   0.9
44   -0.37    0.93   0.9
44   -0.28    0.96    1
44   -0.18    0.98    1
44   -0.08     1      1
44    0.02     1      1
44    0.12    0.99    1
44    0.22    0.98    1
44    0.31    0.95    1
44    0.41    0.91   0.9
45    0.49    0.87   0.9
45    0.58    0.82   0.8
45    0.66    0.75   0.8
45    0.73    0.68   0.7
45    0.79    0.61   0.6
45    0.85    0.53   0.5
45     0.9    0.44   0.4
45    0.94    0.35   0.3
45    0.97    0.25   0.3
45    0.99    0.15   0.2
46      1     0.05   0.1
46      1    -0.05   -0
46    0.99   -0.15   -0
46    0.97   -0.24   -0
46    0.94   -0.34   -0
46     0.9   -0.43   -0
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48   -0.37   -0.93   -1
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48   -0.88   -0.47   -0
48   -0.92   -0.38   -0
48   -0.96   -0.29   -0
49   -0.98   -0.19   -0
49     -1    -0.09   -0
49     -1     0.01    0
49   -0.99    0.11   0.1
49   -0.98     0.2   0.2
49   -0.95     0.3   0.3
49   -0.92    0.39   0.4
49   -0.88    0.48   0.5
49   -0.82    0.57   0.6
49   -0.76    0.65   0.6
50   -0.69    0.72   0.7
50   -0.62    0.79   0.8
50   -0.54    0.84   0.8
50   -0.45    0.89   0.9
50   -0.36    0.93   0.9
50   -0.26    0.96    1
50   -0.16    0.99    1
50   -0.07      1     1
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50    0.13    0.99    1
51    0.23    0.97    1
51    0.33    0.94   0.9
51    0.42    0.91   0.9
51    0.51    0.86   0.9
51    0.59    0.81   0.8
51    0.67    0.74   0.7
51    0.74    0.67   0.7
51    0.8     0.59   0.6
51    0.86    0.51   0.5
51    0.91    0.42   0.4
52    0.94    0.33   0.3
52    0.97    0.23   0.2
52    0.99    0.14   0.1
52     1      0.04    0
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52    0.97   -0.26   -0
52    0.93   -0.36   -0
52    0.89   -0.45   -0
52    0.85   -0.53   -1
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54   -0.78   -0.63   -1
54   -0.84   -0.55   -1
55   -0.89   -0.46   -0
55   -0.93   -0.37   -0
55   -0.96   -0.27   -0
55   -0.98   -0.18   -0
55     -1    -0.08   -0
55     -1     0.02    0
55   -0.99    0.12   0.1
55   -0.98    0.22   0.2
55   -0.95    0.32   0.3
55   -0.91    0.41   0.4
56   -0.87     0.5   0.5
56   -0.81    0.58   0.6
56   -0.75    0.66   0.7
56   -0.68    0.73   0.7
56    -0.6     0.8   0.8
56   -0.52    0.85   0.9
56   -0.43     0.9   0.9
56   -0.34    0.94   0.9
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1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
1   1
-1.92   1
-1.92   1
-1.92   1
-1.92   1
-1.92   1
-1.92   1
-1.92   1
-1.92   1
-1.92   1
-1.92   1
-1.92   1
-1.92   1
-1.92   1
-1.92   1
-1.92   1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
        1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
From centre



              1      0
              1   0.06
                                                      SIMPLE HARMONIC MOTION
Type in required coefficients                                          x =a cos(bt + c)
   a        b        c
   3         1       2
                                                                Displacement - time graph




                                             x
                                                 6

Change the value of c and consider
                                                 5
where the acceleration is pulling the
moving particle.                                 4

Where is the velocity equal to zero?             3
Remember the particle is going up and
down in one spot.                                2
The time axis is artificial.
                                                 1
                                                                                                    Time t
Where is the displacement maximum?
                                                 0
Where is the velocity maximum?          -1            0    1     2       3       4          5   6        7
Minimum?                                         -1
Where is the displacement zero?
                                                 -2
Where is the greatest acceleration?
                                                 -3
Least?
                                                 -4
Experiment.
                                                 -5
What happens to the acceleration when
b > 1? b < 1?                                    -6
Explain precisely.
Starting value
    0            Use 0
Increment
   0.1           Use 0.1




                           4.5
                           4.6
                           4.7
                           4.8
                           4.9
                           5
                           5.1
                           5.2
                           5.3
                           5.4
                           5.5
                           5.6
                           5.7
                           5.8
                           5.9
                           6
                           6.1
                           6.2
                           6.3
                           6.4
                           6.5
                           6.6
                           6.7
6.8
6.9
 7
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
 8
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9
 9
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9
10
10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
10.9
11
11.1
11.2
11.3
11.4
11.5
11.6
11.7
11.8
11.9
12
12.1
12.2
12.3
12.4
12.5
12.6
12.7
12.8
12.9
13
13.1
13.2
13.3
13.4
13.5
13.6
13.7
13.8
13.9
14
14.1
14.2
14.3
14.4
14.5
14.6
14.7
14.8
14.9
15
15.1
15.2
15.3
15.4
15.5
15.6
15.7
15.8
15.9
16
16.1
16.2
16.3
16.4
16.5
16.6
16.7
16.8
16.9
17
17.1
17.2
17.3
17.4
17.5
17.6
17.7
17.8
17.9
18
18.1
18.2
18.3
18.4
18.5
18.6
18.7
18.8
18.9
19
19.1
19.2
19.3
19.4
19.5
19.6
19.7
19.8
19.9
20
20.1
20.2
20.3
20.4
20.5
20.6
20.7
20.8
20.9
21
21.1
21.2
21.3
21.4
21.5
21.6
21.7
21.8
21.9
22
22.1
22.2
22.3
22.4
22.5
22.6
22.7
22.8
22.9
23
23.1
23.2
23.3
23.4
23.5
23.6
23.7
23.8
23.9
24
24.1
24.2
24.3
24.4
24.5
24.6
24.7
24.8
24.9
25
25.1
25.2
25.3
25.4
25.5
25.6
25.7
25.8
25.9
26
26.1
26.2
26.3
26.4
26.5
26.6
26.7
26.8
26.9
27
27.1
27.2
27.3
27.4
27.5
27.6
27.7
27.8
27.9
28
28.1
28.2
28.3
28.4
28.5
28.6
28.7
28.8
28.9
29
29.1
29.2
29.3
29.4
29.5
29.6
29.7
29.8
29.9
30
30.1
30.2
30.3
30.4
30.5
30.6
30.7
30.8
30.9
31
31.1
31.2
31.3
31.4
31.5
31.6
31.7
31.8
31.9
32
32.1
32.2
32.3
32.4
32.5
32.6
32.7
32.8
32.9
33
33.1
33.2
33.3
33.4
33.5
33.6
33.7
33.8
33.9
34
34.1
34.2
34.3
34.4
34.5
34.6
34.7
34.8
34.9
35
35.1
35.2
35.3
35.4
35.5
35.6
35.7
35.8
35.9
36
36.1
36.2
36.3
36.4
36.5
36.6
36.7
36.8
36.9
37
37.1
37.2
37.3
37.4
37.5
37.6
37.7
37.8
37.9
38
38.1
38.2
38.3
38.4
38.5
38.6
38.7
38.8
38.9
39
39.1
39.2
39.3
39.4
39.5
39.6
39.7
39.8
39.9
40
40.1
40.2
40.3
40.4
40.5
40.6
40.7
40.8
40.9
41
41.1
41.2
41.3
41.4
41.5
41.6
41.7
41.8
41.9
42
42.1
42.2
42.3
42.4
42.5
42.6
42.7
42.8
42.9
43
43.1
43.2
43.3
43.4
43.5
43.6
43.7
43.8
43.9
44
44.1
44.2
44.3
44.4
44.5
44.6
44.7
44.8
44.9
45
45.1
45.2
45.3
45.4
45.5
45.6
45.7
45.8
45.9
46
47     47     0.902
47.1   47.1   1.183
47.2   47.2   1.452
47.3   47.3   1.707
47.4   47.4   1.945
47.5   47.5   2.163
47.6   47.6    2.36
47.7   47.7   2.533
47.8   47.8   2.681
47.9   47.9   2.802
48     48     2.895
48.1   48.1   2.959
48.2   48.2   2.994
48.3   48.3   2.998
48.4   48.4   2.973
48.5   48.5   2.918
48.6   48.6   2.834
48.7   48.7   2.721
48.8   48.8   2.582
48.9   48.9   2.416
49     49     2.226
49.1   49.1   2.015
49.2   49.2   1.783
49.3   49.3   1.533
49.4   49.4   1.268
49.5   49.5    0.99
49.6   49.6   0.702
49.7   49.7    0.408
49.8   49.8    0.109
49.9   49.9   -0.191
50     50     -0.489
50.1   50.1   -0.782
50.2   50.2   -1.067
50.3   50.3   -1.342
50.4   50.4   -1.603
50.5   50.5   -1.848
50.6   50.6   -2.075
50.7   50.7   -2.281
50.8   50.8   -2.464
50.9   50.9   -2.623
51     51     -2.755
51.1   51.1    -2.86
51.2   51.2   -2.936
51.3   51.3   -2.983
51.4   51.4       -3
51.5   51.5   -2.987
51.6   51.6   -2.944
51.7   51.7   -2.872
51.8   51.8   -2.771
51.9   51.9   -2.643
52     52     -2.488
52.1   52.1   -2.308
52.2   52.2   -2.105
52.3   52.3   -1.881
52.4   52.4   -1.639
52.5   52.5    -1.38
52.6   52.6   -1.107
52.7   52.7   -0.823
52.8   52.8   -0.531
52.9   52.9   -0.233
53     53      0.066
53.1   53.1    0.365
53.2   53.2    0.661
53.3   53.3     0.95
53.4   53.4    1.229
53.5   53.5    1.496
53.6   53.6    1.748
53.7   53.7    1.983
53.8   53.8    2.198
53.9   53.9    2.391
54     54       2.56
54.1   54.1    2.703
54.2   54.2    2.819
54.3   54.3    2.908
54.4   54.4    2.967
54.5   54.5    2.996
54.6   54.6    2.996
54.7   54.7    2.966
54.8   54.8    2.906
54.9   54.9    2.817
55     55         2.7
55.1   55.1    2.555
55.2   55.2    2.386
55.3   55.3    2.192
55.4   55.4    1.977
55.5   55.5    1.742
55.6   55.6    1.489
55.7   55.7    1.222
55.8   55.8    0.942
55.9   55.9    0.653
56     56      0.358
56.1   56.1    0.058
56.2   56.2   -0.241
56.3   56.3   -0.539
56.4   56.4   -0.831
56.5   56.5   -1.114
56.6   56.6   -1.387
56.7   56.7   -1.645
56.8   56.8   -1.888
56.9   56.9   -2.111
57     57     -2.313
57.1   57.1   -2.492
57.2   57.2   -2.647
57.3   57.3   -2.774
57.4   57.4   -2.875
57.5   57.5   -2.946
57.6   57.6   -2.988
57.7   57.7       -3
57.8   57.8   -2.982
57.9   57.9   -2.934
58     58     -2.857
58.1   58.1   -2.752
58.2   58.2   -2.619
58.3   58.3   -2.459
58.4   58.4   -2.276
58.5   58.5   -2.069
58.6   58.6   -1.842
58.7   58.7   -1.596
58.8   58.8   -1.335
58.9   58.9    -1.06
59     59     -0.774
59.1   59.1   -0.481
59.2   59.2   -0.183
59.3   59.3    0.117
59.4   59.4    0.415
59.5   59.5     0.71
59.6   59.6    0.997
59.7   59.7    1.275
59.8   59.8     1.54
59.9   59.9    1.789
60     60      2.021
60.1   60.1    2.232
60.2   60.2    2.421
60.3   60.3    2.586
60.4   60.4    2.725
60.5   60.5    2.836
60.6   60.6     2.92
60.7   60.7    2.974
60.8   60.8    2.998
60.9   60.9    2.993
61     61      2.958
61.1   61.1    2.893
61.2   61.2    2.799
61.3   61.3    2.677
61.4   61.4    2.529
61.5   61.5    2.355
61.6   61.6    2.158
61.7   61.7    1.939
61.8   61.8       1.7
61.9   61.9    1.445
62     62      1.176
62.1   62.1    0.894
62.2   62.2    0.604
62.3   62.3    0.307
62.4   62.4    0.008
62.5   62.5   -0.292
62.6   62.6   -0.588
62.7   62.7   -0.879
62.8   62.8   -1.161
62.9   62.9   -1.431
63     63     -1.687
63.1   63.1   -1.927
63.2   63.2   -2.147
63.3   63.3   -2.345
63.4   63.4    -2.52
63.5   63.5    -2.67
63.6   63.6   -2.793
63.7   63.7   -2.889
63.8   63.8   -2.955
63.9   63.9   -2.992
64     64     -2.999
64.1   64.1   -2.976
64.2   64.2   -2.923
64.3   64.3   -2.841
64.4   64.4   -2.731
64.5   64.5   -2.594
64.6   64.6    -2.43
64.7   64.7   -2.242
64.8   64.8   -2.032
64.9   64.9   -1.802
65     65     -1.553
65.1   65.1   -1.289
65.2   65.2   -1.012
65.3   65.3   -0.725
65.4   65.4   -0.431
65.5   65.5   -0.133
65.6   65.6    0.167
65.7   65.7    0.465
65.8   65.8    0.759
65.9   65.9    1.045
66     66       1.32
66.1   66.1    1.583
66.2   66.2    1.829
66.3   66.3    2.058
66.4   66.4    2.265
66.5   66.5     2.45
66.6   66.6    2.611
66.7   66.7    2.745
66.8   66.8    2.852
66.9   66.9    2.931
67     67       2.98
67.1   67.1        3
67.2   67.2    2.989
67.3   67.3    2.949
67.4   67.4    2.879
67.5   67.5     2.78
67.6   67.6    2.654
67.7   67.7    2.501
67.8   67.8    2.323
67.9   67.9    2.122
68     68         1.9
68.1   68.1    1.659
68.2   68.2    1.401
68.3   68.3    1.129
68.4   68.4    0.846
68.5   68.5    0.554
68.6   68.6    0.257
68.7   68.7   -0.042
68.8   68.8   -0.342
68.9   68.9   -0.638
69     69     -0.927
69.1   69.1   -1.207
69.2   69.2   -1.475
69.3   69.3   -1.729
69.4   69.4   -1.965
69.5   69.5   -2.181
69.6   69.6   -2.376
69.7   69.7   -2.547
69.8   69.8   -2.693
69.9   69.9   -2.811
70     70     -2.902
70.1   70.1   -2.963
70.2   70.2   -2.995
70.3   70.3   -2.997
70.4   70.4   -2.969
70.5   70.5   -2.912
70.6   70.6   -2.825
70.7   70.7    -2.71
70.8   70.8   -2.568
70.9   70.9      -2.4
71     71     -2.209
71.1   71.1   -1.995
71.2   71.2   -1.761
71.3   71.3    -1.51
71.4   71.4   -1.244
71.5   71.5   -0.965
71.6   71.6   -0.676
71.7   71.7   -0.381
71.8   71.8   -0.082
71.9   71.9    0.218
72     72      0.515
72.1   72.1    0.808
72.2   72.2    1.092
72.3   72.3    1.366
72.4   72.4    1.625
72.5   72.5    1.869
72.6   72.6    2.094
72.7   72.7    2.298
72.8   72.8    2.479
72.9   72.9    2.635
73     73      2.765
73.1   73.1    2.868
73.2   73.2    2.941
73.3   73.3    2.986
73.4   73.4        3
73.5   73.5    2.984
73.6   73.6    2.939
73.7   73.7    2.864
73.8   73.8    2.761
73.9   73.9     2.63
74     74      2.473
74.1   74.1    2.291
74.2   74.2    2.086
74.3   74.3    1.861
74.4   74.4    1.616
74.5   74.5    1.356
74.6   74.6    1.082
74.7   74.7    0.797
74.8   74.8    0.505
74.9   74.9    0.207
75     75     -0.093
75.1   75.1   -0.392
75.2   75.2   -0.687
75.3   75.3   -0.975
75.4   75.4   -1.253
75.5   75.5   -1.519
75.6   75.6    -1.77
75.7   75.7   -2.003
75.8   75.8   -2.216
75.9   75.9   -2.407
76     76     -2.573
76.1   76.1   -2.714
76.2   76.2   -2.828
76.3   76.3   -2.914
76.4   76.4   -2.971
76.5   76.5   -2.998
76.6   76.6   -2.995
76.7   76.7   -2.962
76.8   76.8   -2.899
76.9   76.9   -2.807
77     77     -2.688
77.1   77.1   -2.541
77.2   77.2    -2.37
77.3   77.3   -2.174
77.4   77.4   -1.957
77.5   77.5    -1.72
77.6   77.6   -1.466
77.7   77.7   -1.198
77.8   77.8   -0.917
77.9   77.9   -0.627
78     78     -0.331
78.1   78.1   -0.032
78.2   78.2    0.268
78.3   78.3    0.565
78.4   78.4    0.856
78.5   78.5    1.139
78.6   78.6     1.41
78.7   78.7    1.668
78.8   78.8    1.908
78.9   78.9     2.13
79     79       2.33
79.1   79.1    2.507
79.2   79.2    2.659
79.3   79.3    2.784
79.4   79.4    2.882
79.5   79.5    2.951
79.6   79.6     2.99
79.7   79.7    2.999
79.8   79.8    2.979
79.9   79.9    2.929
80     80      2.849
80.1   80.1    2.741
80.2   80.2    2.606
80.3   80.3    2.444
80.4   80.4    2.258
80.5   80.5     2.05
80.6   80.6    1.821
80.7   80.7    1.574
80.8   80.8    1.311
80.9   80.9    1.035
81     81      0.749
81.1   81.1    0.455
81.2   81.2    0.157
81.3   81.3   -0.143
81.4   81.4   -0.442
81.5   81.5   -0.736
81.6   81.6   -1.022
81.7   81.7   -1.299
81.8   81.8   -1.562
81.9   81.9    -1.81
82     82      -2.04
82.1   82.1   -2.249
82.2   82.2   -2.436
82.3   82.3   -2.599
82.4   82.4   -2.736
82.5   82.5   -2.845
82.6   82.6   -2.926
82.7   82.7   -2.977
82.8   82.8   -2.999
82.9   82.9   -2.991
83     83     -2.953
83.1   83.1   -2.886
83.2   83.2   -2.789
83.3   83.3   -2.665
83.4   83.4   -2.514
83.5   83.5   -2.338
83.6   83.6   -2.139
83.7   83.7   -1.918
83.8   83.8   -1.679
83.9   83.9   -1.422
84     84     -1.151
84.1   84.1   -0.869
84.2   84.2   -0.578
84.3   84.3   -0.281
84.4   84.4    0.019
84.5   84.5    0.318
84.6   84.6    0.614
84.7   84.7    0.904
84.8   84.8    1.185
84.9   84.9    1.455
85     85      1.709
85.1   85.1    1.947
85.2   85.2    2.165
85.3   85.3    2.362
85.4   85.4    2.534
85.5   85.5    2.682
85.6   85.6    2.803
85.7   85.7    2.896
85.8   85.8    2.959
85.9   85.9    2.994
86     86      2.998
86.1   86.1    2.973
86.2   86.2    2.917
86.3   86.3    2.833
86.4   86.4     2.72
86.5   86.5     2.58
86.6   86.6    2.414
86.7   86.7    2.225
86.8   86.8    2.013
86.9   86.9     1.78
87     87      1.531
87.1   87.1    1.265
87.2   87.2    0.987
87.3   87.3       0.7
87.4   87.4    0.405
87.5   87.5    0.106
87.6   87.6   -0.194
87.7   87.7   -0.492
87.8   87.8   -0.785
87.9   87.9    -1.07
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88.1   88.1   -1.605
88.2   88.2    -1.85
88.3   88.3   -2.077
88.4   88.4   -2.283
88.5   88.5   -2.465
88.6   88.6   -2.624
88.7   88.7   -2.756
88.8   88.8    -2.86
88.9   88.9   -2.936
89     89     -2.983
89.1   89.1        -3
89.2   89.2   -2.987
89.3   89.3   -2.944
89.4   89.4   -2.871
89.5   89.5    -2.77
89.6   89.6   -2.642
89.7   89.7   -2.486
89.8   89.8   -2.306
89.9   89.9   -2.103
90     90     -1.879
90.1   90.1   -1.636
90.2   90.2   -1.377
90.3   90.3   -1.104
90.4   90.4    -0.82
90.5   90.5   -0.528
90.6   90.6   -0.231
90.7   90.7    0.069
90.8   90.8    0.368
90.9   90.9    0.664
91     91      0.952
91.1   91.1    1.232
91.2   91.2    1.498
91.3   91.3     1.75
91.4   91.4    1.985
91.5   91.5       2.2
91.6   91.6    2.392
91.7   91.7    2.561
91.8   91.8    2.704
91.9   91.9     2.82
92     92      2.908
92.1   92.1    2.967
92.2   92.2    2.997
92.3   92.3    2.996
92.4   92.4    2.965
92.5   92.5    2.905
92.6   92.6    2.816
92.7   92.7    2.698
92.8   92.8    2.554
92.9   92.9    2.384
93     93      2.191
93.1   93.1    1.975
93.2   93.2     1.74
93.3   93.3    1.487
93.4   93.4    1.219
93.5   93.5     0.94
93.6   93.6    0.651
93.7   93.7    0.355
93.8   93.8    0.056
93.9   93.9   -0.244
94     94     -0.541
94.1   94.1   -0.833
94.2   94.2   -1.117
94.3   94.3   -1.389
94.4   94.4   -1.648
94.5   94.5    -1.89
94.6   94.6   -2.113
94.7   94.7   -2.315
94.8   94.8   -2.494
94.9   94.9   -2.648
95     95     -2.775
95.1   95.1   -2.875
95.2   95.2   -2.946
95.3   95.3   -2.988
95.4   95.4       -3
95.5   95.5   -2.982
95.6   95.6   -2.934
95.7   95.7   -2.856
95.8   95.8   -2.751
95.9   95.9   -2.617
96     96     -2.458
96.1   96.1   -2.274
96.2   96.2   -2.067
96.3   96.3    -1.84
96.4   96.4   -1.594
96.5   96.5   -1.332
96.6   96.6   -1.057
96.7   96.7   -0.772
96.8   96.8   -0.478
96.9   96.9    -0.18
97     97      0.119
97.1   97.1    0.418
97.2   97.2    0.713
97.3   97.3        1
97.4   97.4    1.277
97.5   97.5    1.542
97.6   97.6    1.791
97.7   97.7    2.022
97.8   97.8    2.234
97.9   97.9    2.422
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98.1   98.1    2.726
98.2   98.2    2.837
98.3   98.3     2.92
98.4   98.4    2.974
98.5   98.5    2.999
98.6   98.6    2.993
98.7   98.7    2.957
98.8   98.8    2.892
98.9   98.9    2.798
99     99      2.676
99.1   99.1    2.527
99.2   99.2    2.353
99.3   99.3    2.156
99.4   99.4    1.937
99.5   99.5    1.698
99.6   99.6    1.443
99.7   99.7    1.173
99.8   99.8    0.892
99.9   99.9    0.601
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100.1   100.1    0.005
100.2   100.2   -0.294
100.3   100.3   -0.591
100.4   100.4   -0.882
100.5   100.5   -1.163
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100.9   100.9   -2.148
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101.2   101.2   -2.671
101.3   101.3   -2.794
101.4   101.4   -2.889
101.5   101.5   -2.955
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102.3   102.3   -2.429
102.4   102.4   -2.241
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                       t    x       y             Velocity                                   FIX this column
                            t     a cos(bt+c)     vectors      Speed
                      0     0      -1.2                      | velocity |                      Try 0.157                                                Second derivative
                      0.1   0.1    -1.5             1.00                 Derivative                                  velocity vectors          speed
                      0.2   0.2    -1.8            -2.73        2.905             1   -ab sin(bt+c)                                            \vel\              0
y = a cos(bt + c)     0.3   0.3      -2                                           1     -2.72789 0.1878    -0.512              0   -1.24844     2.905             0
Velocity vector       0.4   0.4    -2.2             1.00                          1     -2.58963 0.1866    -0.483      0.18778     -1.76068     2.776             0
Acceleration vector   0.5   0.5    -2.4            -2.59        2.776             1     -2.42549 0.1849    -0.448     0.375561     -2.27293     2.624             0
                      0.6   0.6    -2.6                                           1     -2.23712 0.1826    -0.408     0.563341     -2.78517     2.45              0
                      0.7   0.7    -2.7             1.00                          1     -2.02639 0.1794    -0.363     0.751121     -3.29742     2.26              0
                      0.8   0.8    -2.8            -2.43        2.624             1     -1.79542 0.1747    -0.314     0.938902     -3.80966     2.055             0
                      0.9   0.9    -2.9                                           1      -1.5465 0.1679      -0.26           1.6   -2.69028     1.842             0
                      1     1        -3                                           1     -1.28214 0.1577    -0.202      1.75975       -2.4782    1.626             0
                      1.1   1.1      -3         Acceleration| acceleration |      1     -1.00496 0.1418    -0.142     1.919499     -2.26612     1.418             0
                      1.2   1.2      -3           vectors                         1     -0.71775 0.1166    -0.084     2.079249     -2.05404     1.231             0
                      1.3   1.3      -3                                           1     -0.42336 0.078     -0.033     2.238998     -1.84197     1.086             0
                      1.4   1.4    -2.9             0.00                          1     -0.12474 0.0248    -0.003     2.398748     -1.62989     1.008             0
                      1.5   1.5    -2.8             1.25        1.248             1    0.175122 0.0345      0.006            3.1   1.133933     1.015             0
                      1.6   1.6    -2.7                                           1    0.473237 0.0856     0.0405     3.288175     1.656578     1.106             0
                      1.7   1.7    -2.5             0.00                          1    0.766623 0.1217     0.0933      3.47635     2.179224     1.26              0
                      1.8   1.8    -2.4             1.51        1.515             1      1.05235 0.145     0.1526     3.664525     2.701869     1.452             0
                      1.9   1.9    -2.2                                           1    1.327561 0.1597     0.2121        3.8527    3.224514     1.662             0
                      2     2        -2             0.00                          1    1.589508 0.1693     0.2691     4.040874     3.747159     1.878             0
                      2.1   2.1    -1.7             1.77        1.766             1    1.835574 0.1756     0.3224                               2.09              0
                      2.2   2.2    -1.5                                           1    2.063298     0.18   0.3713    x going backwards          2.293             0
                      2.3   2.3    -1.2                                           1    2.270407 0.183      0.4156                               2.481             0
                      2.4   2.4    -0.9                                           1    2.454831 0.1852     0.4547                               2.651             0
                      2.5   2.5    -0.6                                           1    2.614727 0.1868     0.4884                               2.799             0
                      2.6   2.6    -0.3                                           1    2.748498 0.1879     0.5166                               2.925             0
                      2.7   2.7      -0                                           1    2.854806 0.1888     0.5389                                                 0
                      2.8   2.8   0.26                                            1      2.93259 0.1893    0.5551                                                 0
                      2.9   2.9   0.56                                            1    2.981073 0.1896     0.5653                                                 0
                      3     3     0.85                                            1      2.99977 0.1897    0.5692                                                 0
                      3.1   3.1   1.13                                            1    2.988494 0.1897     0.5668                                                 0
3.2   3.2   1.41   1   2.947358    0.1894   0.5582    0
3.3   3.3   1.66   1   2.876773    0.1889   0.5435    0
3.4   3.4    1.9   1   2.777444    0.1882   0.5226    0
3.5   3.5   2.13   1   2.650364    0.1871   0.4959    0
3.6   3.6   2.33   1   2.496802    0.1857   0.4636    0
3.7   3.7    2.5   1   2.318293    0.1836   0.4257    0
3.8   3.8   2.66   1   2.116621    0.1808   0.3828    0
3.9   3.9   2.78   1      1.8938   0.1769   0.3349    0
4     4     2.88   1   1.652057    0.1711   0.2827    0
4.1   4.1   2.95   1   1.393807    0.1625   0.2265    0
4.2   4.2   2.99   1    1.12163    0.1493   0.1674    0
4.3   4.3      3   1   0.838246    0.1285   0.1077    0
4.4   4.4   2.98   1   0.546488    0.0959   0.0524    0
4.5   4.5   2.93   1   0.249268    0.0484   0.0121    0
4.6   4.6   2.85   1   -0.05044    0.0101   -5E-04    0
4.7   4.7   2.74   1   -0.34965     0.066    -0.023   0
4.8   4.8   2.61   1   -0.64536    0.1084     -0.07   0
4.9   4.9   2.45   1   -0.93462    0.1366    -0.128   0
5     5     2.26   1   -1.21455    0.1544    -0.188   0
5.1   5.1   2.05   1   -1.48234    0.1658    -0.246   0
5.2   5.2   1.83   1   -1.73532    0.1733    -0.301   0
5.3   5.3   1.58   1   -1.97096    0.1784    -0.352   0
5.4   5.4   1.32   1   -2.18691    0.1819    -0.398   0
5.5   5.5   1.04   1      -2.381   0.1844    -0.439   0
5.6   5.6   0.75   1   -2.55131    0.1862    -0.475   0
5.7   5.7   0.46   1   -2.69612    0.1875    -0.506   0
5.8   5.8   0.16   1      -2.814   0.1885     -0.53   0
5.9   5.9   -0.1   1   -2.90376    0.1891    -0.549   0
6     6     -0.4   1     -2.9645   0.1895    -0.562   0
6.1   6.1   -0.7   1   -2.99563    0.1897    -0.568   0
6.2   6.2     -1   1   -2.99682    0.1897    -0.569   0
6.3   6.3   -1.3   1   -2.96807    0.1895    -0.563   0
6.4   6.4   -1.6   1   -2.90967    0.1891     -0.55   0
6.5   6.5   -1.8   1   -2.82219    0.1885    -0.532   0
6.6   6.6     -2   1   -2.70652    0.1876    -0.508   0
6.7   6.7   -2.2   1     -2.5638   0.1863    -0.478   0
6.8    6.8    -2.4   1   -2.39546    0.1846    -0.442    0
6.9    6.9    -2.6   1   -2.20319    0.1821    -0.401    0
 7      7     -2.7   1   -1.98891    0.1787    -0.355    0
7.1    7.1    -2.8   1   -1.75475    0.1738    -0.305    0
7.2    7.2    -2.9   1   -1.50306    0.1665      -0.25   0
7.3    7.3      -3   1   -1.23636    0.1555    -0.192    0
7.4    7.4      -3   1     -0.9573   0.1383    -0.132    0
7.5    7.5      -3   1   -0.66867    0.1112    -0.074    0
7.6    7.6      -3   1   -0.37336       0.07   -0.026    0
7.7    7.7    -2.9   1   -0.07433    0.0148    -0.001    0
7.8    7.8    -2.8   1   0.225453     0.044    0.0099    0
7.9    7.9    -2.7   1    0.52298    0.0927    0.0485    0
 8      8     -2.5   1   0.815282    0.1264     0.103    0
8.1    8.1    -2.3   1   1.099437     0.148    0.1627    0
8.2    8.2    -2.1   1   1.372608    0.1616    0.2219    0
8.3    8.3    -1.9   1   1.632063    0.1705    0.2783    0
8.4    8.4    -1.7   1   1.875212    0.1765    0.3309    0
8.5    8.5    -1.4   1   2.099624    0.1806    0.3791    0
8.6    8.6    -1.2   1   2.303057    0.1835    0.4225    0
8.7    8.7    -0.9   1   2.483479    0.1855    0.4607    0
8.8    8.8    -0.6   1   2.639087     0.187    0.4936    0
8.9    8.9    -0.3   1   2.768326    0.1881    0.5207    0
 9      9     0.01   1   2.869905    0.1889     0.542    0
9.1    9.1    0.31   1   2.942809    0.1894    0.5573    0
9.2    9.2    0.61   1   2.986309    0.1896    0.5664    0
9.3    9.3     0.9   1   2.999971    0.1897    0.5692    0
9.4    9.4    1.18   1   2.983658    0.1896    0.5658    0
9.5    9.5    1.45   1   2.937533    0.1893    0.5562    0
9.6    9.6     1.7   1   2.862058    0.1888    0.5404    0
9.7    9.7    1.94   1   2.757986     0.188    0.5186    0
9.8    9.8    2.16   1   2.626357    0.1869    0.4909    0
9.9    9.9    2.36   1   2.468486    0.1854    0.4576    0
10     10     2.53   1   2.285951    0.1832    0.4189    0
10.1   10.1   2.68   1   2.080575    0.1803     0.375    0
10.2   10.2    2.8   1   1.854411     0.176    0.3264    0
10.3   10.3   2.89   1   1.609719    0.1699    0.2735    0
10.4   10.4   2.96   1   1.348942    0.1607   0.2167    0
10.5   10.5   2.99   1   1.074688    0.1464   0.1574    0
10.6   10.6      3   1   0.789695     0.124   0.0979    0
10.7   10.7   2.97   1   0.496813     0.089   0.0442    0
10.8   10.8   2.92   1   0.198966     0.039   0.0078    0
10.9   10.9   2.83   1   -0.10087    0.0201   -0.002    0
11     11     2.72   1     -0.3997   0.0742     -0.03   0
11.1   11.1   2.58   1   -0.69453    0.1141   -0.079    0
11.2   11.2   2.42   1   -0.98242    0.1402   -0.138    0
11.3   11.3   2.23   1     -1.2605   0.1567   -0.197    0
11.4   11.4   2.02   1   -1.52598    0.1673   -0.255    0
11.5   11.5   1.78   1   -1.77622    0.1743     -0.31   0
11.6   11.6   1.54   1   -2.00871     0.179     -0.36   0
11.7   11.7   1.27   1   -2.22113    0.1824   -0.405    0
11.8   11.8   0.99   1   -2.41135    0.1847   -0.445    0
11.9   11.9    0.7   1   -2.57749    0.1865   -0.481    0
12     12     0.41   1   -2.71786    0.1877     -0.51   0
12.1   12.1   0.11   1   -2.83109    0.1886   -0.534    0
12.2   12.2   -0.2   1   -2.91602    0.1892   -0.552    0
12.3   12.3   -0.5   1   -2.97182    0.1896   -0.563    0
12.4   12.4   -0.8   1   -2.99793    0.1897   -0.569    0
12.5   12.5   -1.1   1   -2.99408    0.1897   -0.568    0
12.6   12.6   -1.3   1   -2.96032    0.1895   -0.561    0
12.7   12.7   -1.6   1   -2.89697    0.1891   -0.548    0
12.8   12.8   -1.8   1   -2.80469    0.1884   -0.528    0
12.9   12.9   -2.1   1   -2.68437    0.1874   -0.503    0
13     13     -2.3   1   -2.53724    0.1861   -0.472    0
13.1   13.1   -2.5   1   -2.36476    0.1842   -0.436    0
13.2   13.2   -2.6   1   -2.16864    0.1816   -0.394    0
13.3   13.3   -2.8   1   -1.95086     0.178   -0.347    0
13.4   13.4   -2.9   1   -1.71359    0.1727   -0.296    0
13.5   13.5   -2.9   1     -1.4592    0.165   -0.241    0
13.6   13.6     -3   1   -1.19022    0.1531   -0.182    0
13.7   13.7     -3   1   -0.90936    0.1346   -0.122    0
13.8   13.8     -3   1     -0.6194   0.1053   -0.065    0
13.9   13.9   -2.9   1   -0.32326    0.0615     -0.02   0
14     14     -2.9   1   -0.02389    0.0048   -1E-04    0
14.1   14.1   -2.8   1   0.275721    0.0532   0.0147    0
14.2   14.2   -2.6   1   0.572576    0.0994   0.0569    0
14.3   14.3   -2.5   1    0.86371    0.1307   0.1129    0
14.4   14.4   -2.3   1   1.146214    0.1507   0.1727    0
14.5   14.5   -2.1   1   1.417266    0.1634   0.2316    0
14.6   14.6   -1.9   1   1.674157    0.1717   0.2875    0
14.7   14.7   -1.6   1    1.91432    0.1773   0.3394    0
14.8   14.8   -1.4   1   2.135356    0.1811   0.3868    0
14.9   14.9   -1.1   1   2.335056    0.1839   0.4293    0
15     15     -0.8   1   2.511425    0.1858   0.4667    0
15.1   15.1   -0.5   1   2.662701    0.1872   0.4985    0
15.2   15.2   -0.2   1   2.787372    0.1883   0.5247    0
15.3   15.3   0.06   1   2.884192     0.189     0.545   0
15.4   15.4   0.36   1   2.952195    0.1894   0.5592    0
15.5   15.5   0.66   1      2.9907   0.1897   0.5673    0
15.6   15.6   0.95   1   2.999323    0.1897   0.5691    0
15.7   15.7   1.23   1   2.977978    0.1896   0.5646    0
15.8   15.8   1.49   1   2.926878    0.1893   0.5539    0
15.9   15.9   1.75   1   2.846533    0.1887   0.5371    0
16     16     1.98   1   2.737747    0.1879   0.5143    0
16.1   16.1    2.2   1   2.601607    0.1867   0.4857    0
16.2   16.2   2.39   1   2.439471    0.1851   0.4514    0
16.3   16.3   2.56   1   2.252962    0.1828   0.4118    0
16.4   16.4    2.7   1   2.043941    0.1797   0.3672    0
16.5   16.5   2.82   1   1.814498    0.1752   0.3178    0
16.6   16.6   2.91   1   1.566926    0.1686   0.2642    0
16.7   16.7   2.97   1   1.303697    0.1587   0.2069    0
16.8   16.8      3   1   1.027442    0.1433   0.1473    0
16.9   16.9      3   1   0.740921    0.1191   0.0882    0
17     17     2.97   1   0.446997    0.0816   0.0365    0
17.1   17.1   2.91   1   0.148607    0.0294   0.0044    0
17.2   17.2   2.82   1   -0.15127    0.0299    -0.005   0
17.3   17.3    2.7   1   -0.44963     0.082    -0.037   0
17.4   17.4   2.56   1     -0.7435   0.1193    -0.089   0
17.5   17.5   2.39   1   -1.02994    0.1435    -0.148   0
17.6   17.6   2.19   1     -1.3061   0.1588   -0.207   0
17.7   17.7   1.98   1     -1.5692   0.1687   -0.265   0
17.8   17.8   1.74   1   -1.81662    0.1752   -0.318   0
17.9   17.9   1.49   1   -2.04589    0.1797   -0.368   0
18     18     1.22   1   -2.25472    0.1828   -0.412   0
18.1   18.1   0.94   1   -2.44102    0.1851   -0.452   0
18.2   18.2   0.66   1   -2.60293    0.1867   -0.486   0
18.3   18.3   0.36   1   -2.73884    0.1879   -0.515   0
18.4   18.4   0.06   1   -2.84737    0.1887   -0.537   0
18.5   18.5   -0.2   1   -2.92746    0.1893   -0.554   0
18.6   18.6   -0.5   1     -2.9783   0.1896   -0.565   0
18.7   18.7   -0.8   1   -2.99938    0.1897   -0.569   0
18.8   18.8   -1.1   1   -2.99049    0.1897   -0.567   0
18.9   18.9   -1.4   1   -2.95172    0.1894   -0.559   0
19     19     -1.6   1   -2.88346     0.189   -0.545   0
19.1   19.1   -1.9   1   -2.78639    0.1882   -0.525   0
19.2   19.2   -2.1   1   -2.66147    0.1872   -0.498   0
19.3   19.3   -2.3   1   -2.50997    0.1858   -0.466   0
19.4   19.4   -2.5   1   -2.33338    0.1838   -0.429   0
19.5   19.5   -2.6   1   -2.13348    0.1811   -0.386   0
19.6   19.6   -2.8   1   -1.91227    0.1772   -0.339   0
19.7   19.7   -2.9   1   -1.67195    0.1716   -0.287   0
19.8   19.8   -2.9   1   -1.41492    0.1633   -0.231   0
19.9   19.9     -3   1   -1.14375    0.1506   -0.172   0
20     20       -3   1   -0.86116    0.1305   -0.112   0
20.1   20.1     -3   1   -0.56996     0.099   -0.056   0
20.2   20.2   -2.9   1   -0.27307    0.0527   -0.014   0
20.3   20.3   -2.9   1   0.026554    0.0053   0.0001   0
20.4   20.4   -2.8   1    0.32591     0.062   0.0202   0
20.5   20.5   -2.6   1   0.622009    0.1056   0.0657   0
20.6   20.6   -2.5   1   0.911894    0.1348   0.1229   0
20.7   20.7   -2.3   1   1.192667    0.1533   0.1828   0
20.8   20.8   -2.1   1   1.461524    0.1651   0.2412   0
20.9   20.9   -1.8   1   1.715777    0.1728   0.2965   0
21     21     -1.6   1   1.952887     0.178   0.3476   0
21.1   21.1   -1.3   1   2.170484    0.1816   0.3943   0
21.2   21.2   -1.1   1   2.366395    0.1842     0.436   0
21.3   21.3   -0.8   1   2.538661    0.1861    0.4724   0
21.4   21.4   -0.5   1   2.685562    0.1874    0.5033   0
21.5   21.5   -0.2   1    2.80563    0.1884    0.5286   0
21.6   21.6   0.11   1   2.897664    0.1891    0.5478   0
21.7   21.7   0.41   1   2.960747    0.1895     0.561   0
21.8   21.8   0.71   1   2.994246    0.1897     0.568   0
21.9   21.9   0.99   1   2.997828    0.1897    0.5688   0
22     22     1.27   1   2.971457    0.1896    0.5633   0
22.1   22.1   1.54   1   2.915395    0.1892    0.5515   0
22.2   22.2   1.79   1   2.830204    0.1886    0.5337   0
22.3   22.3   2.02   1   2.716735    0.1877    0.5099   0
22.4   22.4   2.23   1   2.576121    0.1864    0.4803   0
22.5   22.5   2.42   1   2.409767    0.1847    0.4451   0
22.6   22.6   2.58   1   2.219336    0.1823    0.4047   0
22.7   22.7   2.72   1   2.006729     0.179    0.3592   0
22.8   22.8   2.84   1   1.774073    0.1742    0.3091   0
22.9   22.9   2.92   1    1.52369    0.1672    0.2548   0
23     23     2.97   1   1.258083    0.1566     0.197   0
23.1   23.1      3   1   0.979905       0.14   0.1372   0
23.2   23.2   2.99   1   0.691937    0.1138    0.0787   0
23.3   23.3   2.96   1   0.397055    0.0738    0.0293   0
23.4   23.4   2.89   1   0.098206    0.0195    0.0019   0
23.5   23.5    2.8   1   -0.20162    0.0395    -0.008   0
23.6   23.6   2.68   1   -0.49944    0.0894    -0.045   0
23.7   23.7   2.53   1   -0.79227    0.1242    -0.098   0
23.8   23.8   2.36   1   -1.07718    0.1466    -0.158   0
23.9   23.9   2.16   1   -1.35132    0.1608    -0.217   0
24     24     1.94   1   -1.61197       0.17   -0.274   0
24.1   24.1    1.7   1   -1.85651    0.1761    -0.327   0
24.2   24.2   1.45   1   -2.08249    0.1803    -0.375   0
24.3   24.3   1.18   1   -2.28768    0.1833    -0.419   0
24.4   24.4    0.9   1       -2.47   0.1854    -0.458   0
24.5   24.5   0.61   1   -2.62764    0.1869    -0.491   0
24.6   24.6   0.31   1   -2.75903     0.188    -0.519   0
24.7   24.7   0.01   1   -2.86286    0.1888    -0.541   0
24.8   24.8   -0.3   1   -2.93807    0.1893   -0.556    0
24.9   24.9   -0.6   1   -2.98393    0.1896   -0.566    0
25     25     -0.9   1   -2.99998    0.1897   -0.569    0
25.1   25.1   -1.2   1   -2.98605    0.1896   -0.566    0
25.2   25.2   -1.4   1   -2.94229    0.1894   -0.557    0
25.3   25.3   -1.7   1   -2.86913    0.1889   -0.542    0
25.4   25.4   -1.9   1     -2.7673   0.1881   -0.521    0
25.5   25.5   -2.1   1   -2.63782     0.187   -0.493    0
25.6   25.6   -2.3   1   -2.48198    0.1855     -0.46   0
25.7   25.7   -2.5   1   -2.30135    0.1834   -0.422    0
25.8   25.8   -2.7   1   -2.09772    0.1805   -0.379    0
25.9   25.9   -2.8   1   -1.87313    0.1764     -0.33   0
26     26     -2.9   1   -1.62983    0.1705   -0.278    0
26.1   26.1     -3   1   -1.37024    0.1616   -0.221    0
26.2   26.2     -3   1   -1.09696    0.1478   -0.162    0
26.3   26.3     -3   1   -0.81272    0.1261   -0.103    0
26.4   26.4     -3   1   -0.52036    0.0923   -0.048    0
26.5   26.5   -2.9   1     -0.2228   0.0435     -0.01   0
26.6   26.6   -2.8   1    0.07699    0.0154   0.0012    0
26.7   26.7   -2.7   1   0.376007    0.0704   0.0265    0
26.8   26.8   -2.6   1   0.671267    0.1115   0.0748    0
26.9   26.9   -2.4   1    0.95982    0.1385   0.1329    0
27     27     -2.2   1   1.238783    0.1556   0.1928    0
27.1   27.1     -2   1   1.505368    0.1666   0.2508    0
27.2   27.2   -1.8   1   1.756912    0.1738   0.3054    0
27.3   27.3   -1.6   1   1.990902    0.1787   0.3558    0
27.4   27.4   -1.3   1   2.204999    0.1821   0.4016    0
27.5   27.5     -1   1   2.397064    0.1846   0.4425    0
27.6   27.6   -0.7   1   2.565179    0.1863    0.478    0
27.7   27.7   -0.4   1   2.707664    0.1876    0.508    0
27.8   27.8   -0.1   1   2.823094    0.1885   0.5322    0
27.9   27.9   0.16   1   2.910317    0.1891   0.5505    0
28     28     0.46   1   2.968461    0.1895   0.5626    0
28.1   28.1   0.76   1   2.996945    0.1897   0.5686    0
28.2   28.2   1.04   1   2.995485    0.1897   0.5683    0
28.3   28.3   1.32   1   2.964095    0.1895   0.5617    0
28.4   28.4   1.58   1   2.903088    0.1891    0.549   0
28.5   28.5   1.83   1   2.813075    0.1884   0.5301   0
28.6   28.6   2.06   1   2.694955    0.1875   0.5053   0
28.7   28.7   2.26   1   2.549907    0.1862   0.4748   0
28.8   28.8   2.45   1   2.379382    0.1844   0.4387   0
28.9   28.9   2.61   1   2.185082    0.1819   0.3974   0
29     29     2.74   1    1.96895    0.1783   0.3511   0
29.1   29.1   2.85   1   1.733145    0.1732   0.3002   0
29.2   29.2   2.93   1   1.480023    0.1657   0.2453   0
29.3   29.3   2.98   1   1.212113    0.1543    0.187   0
29.4   29.4      3   1   0.932092    0.1364   0.1271   0
29.5   29.5   2.99   1   0.642758    0.1081   0.0695   0
29.6   29.6   2.95   1   0.347001    0.0656   0.0228   0
29.7   29.7   2.88   1   0.047778    0.0095   0.0005   0
29.8   29.8   2.78   1   -0.25192    0.0489   -0.012   0
29.9   29.9   2.66   1   -0.54911    0.0963   -0.053   0
30     30      2.5   1     -0.8408   0.1287   -0.108   0
30.1   30.1   2.33   1     -1.1241   0.1494   -0.168   0
30.2   30.2   2.12   1   -1.39617    0.1626   -0.227   0
30.3   30.3    1.9   1   -1.65428    0.1712   -0.283   0
30.4   30.4   1.66   1   -1.89587    0.1769   -0.335   0
30.5   30.5    1.4   1   -2.11851    0.1809   -0.383   0
30.6   30.6   1.13   1   -2.31998    0.1837   -0.426   0
30.7   30.7   0.85   1   -2.49828    0.1857   -0.464   0
30.8   30.8   0.56   1   -2.65161    0.1871   -0.496   0
30.9   30.9   0.26   1   -2.77845    0.1882   -0.523   0
31     31       -0   1   -2.87753    0.1889   -0.544   0
31.1   31.1   -0.3   1   -2.94785    0.1894   -0.558   0
31.2   31.2   -0.6   1   -2.98873    0.1897   -0.567   0
31.3   31.3   -0.9   1   -2.99974    0.1897   -0.569   0
31.4   31.4   -1.2   1   -2.98077    0.1896   -0.565   0
31.5   31.5   -1.5   1   -2.93203    0.1893   -0.555   0
31.6   31.6   -1.7   1   -2.85399    0.1887   -0.539   0
31.7   31.7     -2   1   -2.74743    0.1879   -0.516   0
31.8   31.8   -2.2   1   -2.61342    0.1868   -0.488   0
31.9   31.9   -2.4   1     -2.4533   0.1852   -0.454   0
32     32     -2.5   1   -2.26866     0.183   -0.415    0
32.1   32.1   -2.7   1   -2.06136    0.1799   -0.371    0
32.2   32.2   -2.8   1   -1.83347    0.1756   -0.322    0
32.3   32.3   -2.9   1   -1.58725    0.1692   -0.269    0
32.4   32.4     -3   1   -1.32517    0.1596   -0.212    0
32.5   32.5     -3   1   -1.04985    0.1448   -0.152    0
32.6   32.6     -3   1   -0.76405    0.1214   -0.093    0
32.7   32.7     -3   1   -0.47061    0.0852     -0.04   0
32.8   32.8   -2.9   1   -0.17246     0.034   -0.006    0
32.9   32.9   -2.8   1   0.127404    0.0253   0.0032    0
33     33     -2.7   1   0.425998    0.0784   0.0334    0
33.1   33.1   -2.6   1   0.720335    0.1169   0.0842    0
33.2   33.2   -2.4   1   1.007475    0.1419    0.143    0
33.3   33.3   -2.2   1   1.284548    0.1578   0.2027    0
33.4   33.4     -2   1   1.548787     0.168   0.2602    0
33.5   33.5   -1.8   1    1.79755    0.1748   0.3142    0
33.6   33.6   -1.5   1   2.028354    0.1794   0.3639    0
33.7   33.7   -1.2   1    2.23889    0.1826   0.4088    0
33.8   33.8     -1   1   2.427056    0.1849   0.4488    0
33.9   33.9   -0.7   1   2.590972    0.1866   0.4834    0
34     34     -0.4   1       2.729   0.1878   0.5125    0
34.1   34.1   -0.1   1   2.839761    0.1886   0.5357    0
34.2   34.2   0.21   1   2.922147    0.1892   0.5529    0
34.3   34.3   0.51   1   2.975337    0.1896   0.5641    0
34.4   34.4   0.81   1   2.998797    0.1897    0.569    0
34.5   34.5   1.09   1   2.992295    0.1897   0.5676    0
34.6   34.6   1.36   1   2.955895    0.1895      0.56   0
34.7   34.7   1.62   1   2.889961     0.189   0.5462    0
34.8   34.8   1.87   1   2.795151    0.1883   0.5264    0
34.9   34.9   2.09   1   2.672412    0.1873   0.5006    0
35     35      2.3   1   2.522972    0.1859   0.4691    0
35.1   35.1   2.48   1   2.348324     0.184   0.4321    0
35.2   35.2   2.63   1   2.150211    0.1813   0.3899    0
35.3   35.3   2.76   1   1.930614    0.1776   0.3429    0
35.4   35.4   2.87   1   1.691728    0.1722   0.2913    0
35.5   35.5   2.94   1   1.435938    0.1641   0.2357    0
35.6   35.6   2.99   1    1.1658 0.1518 0.177    0
35.7   35.7      3   1 0.884015 0.1325 0.1171    0
35.8   35.8   2.98   1 0.593396 0.1021 0.0606    0
35.9   35.9   2.94   1 0.296849 0.0569 0.0169    0
36     36     2.87   1 -0.00266 0.0005 -1E-06    0
36.1   36.1   2.76   1 -0.30215 0.0578 -0.017    0
36.2   36.2   2.63   1 -0.59862 0.1027 -0.061    0
36.3   36.3   2.47   1 -0.88911 0.1329 -0.118    0
36.4   36.4   2.29   1 -1.17071 0.1521 -0.178    0
36.5   36.5   2.09   1 -1.44061 0.1643 -0.237    0
36.6   36.6   1.86   1 -1.69613 0.1723 -0.292    0
36.7   36.7   1.62   1 -1.93469 0.1777 -0.344    0
36.8   36.8   1.36   1 -2.15392 0.1814 -0.391    0
36.9   36.9   1.08   1 -2.35164 0.1841 -0.433    0
37     37      0.8   1 -2.52585 0.186    -0.47   0
37.1   37.1   0.51   1 -2.67483 0.1873 -0.501    0
37.2   37.2   0.21   1 -2.79708 0.1883 -0.527    0
37.3   37.3   -0.1   1 -2.89139 0.189 -0.547     0
37.4   37.4   -0.4   1   -2.9568 0.1895  -0.56   0
37.5   37.5   -0.7   1 -2.99267 0.1897 -0.568    0
37.6   37.6     -1   1 -2.99864 0.1897 -0.569    0
37.7   37.7   -1.3   1 -2.97465 0.1896 -0.564    0
37.8   37.8   -1.5   1 -2.92094 0.1892 -0.553    0
37.9   37.9   -1.8   1 -2.83804 0.1886 -0.535    0
38     38       -2   1 -2.72678 0.1878 -0.512    0
38.1   38.1   -2.2   1 -2.58828 0.1866 -0.483    0
38.2   38.2   -2.4   1 -2.42392 0.1849 -0.448    0
38.3   38.3   -2.6   1 -2.23534 0.1826 -0.408    0
38.4   38.4   -2.7   1 -2.02442 0.1793 -0.363    0
38.5   38.5   -2.8   1 -1.79328 0.1747 -0.313    0
38.6   38.6   -2.9   1 -1.54422 0.1679 -0.259    0
38.7   38.7     -3   1 -1.27973 0.1576 -0.202    0
38.8   38.8     -3   1 -1.00245 0.1416 -0.142    0
38.9   38.9     -3   1 -0.71516 0.1163 -0.083    0
39     39       -3   1 -0.42072 0.0776 -0.033    0
39.1   39.1   -2.9   1 -0.12208 0.0242 -0.003    0
39.2   39.2   -2.8   1   0.177782    0.035    0.0062    0
39.3   39.3   -2.7   1   0.475868   0.0859    0.0409    0
39.4   39.4   -2.5   1   0.769199   0.1219    0.0938    0
39.5   39.5   -2.4   1   1.054844   0.1451    0.1531    0
39.6   39.6   -2.2   1    1.32995   0.1599    0.2126    0
39.7   39.7     -2   1   1.591768   0.1694    0.2696    0
39.8   39.8   -1.7   1    1.83768   0.1757    0.3228    0
39.9   39.9   -1.5   1   2.065232      0.18   0.3718    0
40     40     -1.2   1   2.272148   0.1831    0.4159    0
40.1   40.1   -0.9   1   2.456362   0.1852      0.455   0
40.2   40.2   -0.6   1   2.616033   0.1868    0.4887    0
40.3   40.3   -0.3   1   2.749565    0.188    0.5168    0
40.4   40.4     -0   1   2.855624   0.1888      0.539   0
40.5   40.5   0.27   1   2.933151   0.1893    0.5552    0
40.6   40.6   0.56   1   2.981371   0.1896    0.5653    0
40.7   40.7   0.85   1   2.999802   0.1897    0.5692    0
40.8   40.8   1.14   1    2.98826   0.1897    0.5668    0
40.9   40.9   1.41   1    2.94686   0.1894    0.5581    0
41     41     1.67   1   2.876016   0.1889    0.5433    0
41.1   41.1   1.91   1   2.776436   0.1882    0.5224    0
41.2   41.2   2.13   1   2.649115   0.1871    0.4957    0
41.3   41.3   2.33   1   2.495324   0.1856    0.4633    0
41.4   41.4   2.51   1   2.316601   0.1836    0.4254    0
41.5   41.5   2.66   1   2.114732   0.1808    0.3824    0
41.6   41.6   2.78   1   1.891733   0.1768    0.3345    0
41.7   41.7   2.88   1   1.649832    0.171    0.2822    0
41.8   41.8   2.95   1   1.391447   0.1624      0.226   0
41.9   41.9   2.99   1   1.119158   0.1491    0.1669    0
42     42        3   1   0.835688   0.1283    0.1072    0
42.1   42.1   2.98   1   0.543867   0.0956      0.052   0
42.2   42.2   2.93   1   0.246613   0.0479    0.0118    0
42.3   42.3   2.85   1   -0.05311   0.0106    -6E-04    0
42.4   42.4   2.74   1   -0.35229   0.0665     -0.023   0
42.5   42.5   2.61   1   -0.64796   0.1088      -0.07   0
42.6   42.6   2.45   1   -0.93716   0.1368     -0.128   0
42.7   42.7   2.26   1   -1.21699   0.1545     -0.188   0
42.8   42.8   2.05   1   -1.48466    0.1659   -0.246    0
42.9   42.9   1.82   1   -1.73749    0.1733   -0.301    0
43     43     1.58   1   -1.97297    0.1784   -0.352    0
43.1   43.1   1.31   1   -2.18873    0.1819   -0.398    0
43.2   43.2   1.04   1   -2.38262    0.1844   -0.439    0
43.3   43.3   0.75   1   -2.55271    0.1862   -0.475    0
43.4   43.4   0.46   1   -2.69729    0.1875   -0.506    0
43.5   43.5   0.16   1   -2.81492    0.1885   -0.531    0
43.6   43.6   -0.1   1   -2.90443    0.1891   -0.549    0
43.7   43.7   -0.4   1   -2.96491    0.1895   -0.562    0
43.8   43.8   -0.7   1   -2.99577    0.1897   -0.568    0
43.9   43.9     -1   1     -2.9967   0.1897   -0.569    0
44     44     -1.3   1   -2.96769    0.1895   -0.562    0
44.1   44.1   -1.6   1   -2.90902    0.1891     -0.55   0
44.2   44.2   -1.8   1   -2.82129    0.1885   -0.532    0
44.3   44.3     -2   1   -2.70537    0.1876   -0.508    0
44.4   44.4   -2.2   1   -2.56241    0.1863   -0.477    0
44.5   44.5   -2.4   1   -2.39386    0.1845   -0.442    0
44.6   44.6   -2.6   1   -2.20138    0.1821   -0.401    0
44.7   44.7   -2.7   1   -1.98691    0.1786   -0.355    0
44.8   44.8   -2.8   1   -1.75259    0.1737   -0.304    0
44.9   44.9   -2.9   1   -1.50076    0.1664     -0.25   0
45     45       -3   1   -1.23393    0.1554   -0.192    0
45.1   45.1     -3   1   -0.95477    0.1381   -0.132    0
45.2   45.2     -3   1   -0.66607    0.1109   -0.074    0
45.3   45.3     -3   1   -0.37072    0.0695   -0.026    0
45.4   45.4   -2.9   1   -0.07166    0.0143   -0.001    0
45.5   45.5   -2.8   1    0.22811    0.0445   0.0101    0
45.6   45.6   -2.7   1   0.525604    0.0931   0.0489    0
45.7   45.7   -2.5   1   0.817846    0.1266   0.1036    0
45.8   45.8   -2.3   1   1.101916    0.1481   0.1632    0
45.9   45.9   -2.1   1   1.374976    0.1617   0.2224    0
46     46     -1.9   1   1.634298    0.1706   0.2788    0
46.1   46.1   -1.7   1   1.877291    0.1765   0.3314    0
46.2   46.2   -1.4   1   2.101526    0.1806   0.3795    0
46.3   46.3   -1.2   1   2.304764    0.1835   0.4229    0
46.4   46.4   -0.9   1   2.484973    0.1855   0.4611    0
46.5   46.5   -0.6   1   2.640353     0.187   0.4938    0
46.6   46.6   -0.3   1   2.769352    0.1881   0.5209    0
46.7   46.7   0.02   1    2.87068    0.1889   0.5422    0
46.8   46.8   0.32   1   2.943325    0.1894   0.5574    0
46.9   46.9   0.61   1   2.986562    0.1897   0.5664    0
              -1.2   1   2.999958    0.1897   0.5692    0
              -1.2   1   2.983379    0.1896   0.5657    0
              -1.2   1   2.936991    0.1893   0.5561    0
              -1.2   1   2.861258    0.1888   0.5402    0
              -1.2   1   2.756936     0.188   0.5183    0
              -1.2   1   2.625068    0.1869   0.4906    0
              -1.2   1   2.466971    0.1854   0.4573    0
              -1.2   1   2.284224    0.1832   0.4185    0
              -1.2   1   2.078655    0.1802   0.3746    0
              -1.2   1   1.852316     0.176    0.326    0
              -1.2   1    1.60747    0.1698    0.273    0
              -1.2   1   1.346562    0.1606   0.2162    0
              -1.2   1      1.0722   0.1463   0.1568    0
              -1.2   1   0.787125    0.1237   0.0974    0
              -1.2   1   0.494185    0.0886   0.0438    0
              -1.2   1   0.196307    0.0385   0.0076    0
              -1.2   1   -0.10353    0.0206   -0.002    0
              -1.2   1   -0.40234    0.0747     -0.03   0
              -1.2   1   -0.69712    0.1144     -0.08   0
              -1.2   1   -0.98494    0.1403   -0.138    0
              -1.2   1   -1.26292    0.1568   -0.198    0
              -1.2   1   -1.52828    0.1674   -0.256    0
              -1.2   1   -1.77837    0.1743     -0.31   0
              -1.2   1   -2.01069    0.1791     -0.36   0
              -1.2   1   -2.22292    0.1824   -0.405    0
              -1.2   1   -2.41294    0.1848   -0.446    0
              -1.2   1   -2.57885    0.1865   -0.481    0
              -1.2   1   -2.71899    0.1877     -0.51   0
              -1.2   1   -2.83197    0.1886   -0.534    0
              -1.2   1   -2.91665    0.1892   -0.552    0
-1.2   1   -2.97219    0.1896    -0.563   0
-1.2   1   -2.99803    0.1897    -0.569   0
-1.2   1   -2.99391    0.1897    -0.568   0
-1.2   1   -2.95988    0.1895    -0.561   0
-1.2   1   -2.89628     0.189    -0.548   0
-1.2   1   -2.80374    0.1884    -0.528   0
-1.2   1   -2.68318    0.1874    -0.503   0
-1.2   1   -2.53582    0.1861    -0.472   0
-1.2   1   -2.36312    0.1842    -0.435   0
-1.2   1     -2.1668   0.1816    -0.393   0
-1.2   1   -1.94884    0.1779    -0.347   0
-1.2   1     -1.7114   0.1727    -0.296   0
-1.2   1   -1.45687    0.1649     -0.24   0
-1.2   1   -1.18778     0.153    -0.182   0
-1.2   1   -0.90682    0.1343    -0.122   0
-1.2   1     -0.6168    0.105    -0.065   0
-1.2   1   -0.32061    0.0611     -0.02   0
-1.2   1   -0.02123    0.0042   -9E-05    0
-1.2   1   0.278374    0.0536   0.0149    0
-1.2   1   0.575191    0.0997   0.0574    0
-1.2   1   0.866261     0.131   0.1134    0
-1.2   1   1.148676    0.1508   0.1733    0
-1.2   1   1.419614    0.1635   0.2321    0
-1.2   1   1.676367    0.1718   0.2879    0
-1.2   1   1.916371    0.1773   0.3398    0
-1.2   1   2.137227    0.1812   0.3872    0
-1.2   1   2.336728    0.1839   0.4297    0
-1.2   1   2.512882    0.1858     0.467   0
-1.2   1   2.663928    0.1872   0.4988    0
-1.2   1   2.788356    0.1883   0.5249    0
-1.2   1   2.884925     0.189   0.5452    0
-1.2   1   2.952668    0.1894   0.5593    0
-1.2   1   2.990909    0.1897   0.5673    0
-1.2   1   2.999266    0.1897   0.5691    0
-1.2   1   2.977655    0.1896   0.5645    0
-1.2   1   2.926292    0.1893   0.5538    0
-1.2   1   2.845691    0.1887   0.5369   0
-1.2   1   2.736657    0.1879   0.5141   0
-1.2   1   2.600279    0.1867   0.4854   0
-1.2   1    2.43792     0.185   0.4511   0
-1.2   1   2.251201    0.1828   0.4115   0
-1.2   1    2.04199    0.1796   0.3668   0
-1.2   1   1.812376    0.1751   0.3174   0
-1.2   1   1.564653    0.1685   0.2637   0
-1.2   1   1.301297    0.1586   0.2064   0
-1.2   1   1.024938    0.1432   0.1467   0
-1.2   1   0.738339    0.1188   0.0877   0
-1.2   1   0.444362    0.0812   0.0361   0
-1.2   1   0.145946    0.0289   0.0042   0
-1.2   1   -0.15393    0.0304   -0.005   0
-1.2   1   -0.45227    0.0824   -0.037   0
-1.2   1   -0.74608    0.1196   -0.089   0
-1.2   1   -1.03245    0.1437   -0.148   0
-1.2   1   -1.30849    0.1589   -0.208   0
-1.2   1   -1.57147    0.1687   -0.265   0
-1.2   1   -1.81874    0.1753   -0.319   0
-1.2   1   -2.04784    0.1797   -0.368   0
-1.2   1   -2.25648    0.1828   -0.413   0
-1.2   1   -2.44257    0.1851   -0.452   0
-1.2   1   -2.60426    0.1867   -0.486   0
-1.2   1   -2.73992    0.1879   -0.515   0
-1.2   1   -2.84821    0.1887   -0.537   0
-1.2   1   -2.92804    0.1893   -0.554   0
-1.2   1   -2.97862    0.1896   -0.565   0
-1.2   1   -2.99943    0.1897   -0.569   0
-1.2   1   -2.99028    0.1897   -0.567   0
-1.2   1   -2.95124    0.1894   -0.559   0
-1.2   1   -2.88272     0.189   -0.545   0
-1.2   1     -2.7854   0.1882   -0.524   0
-1.2   1   -2.66024    0.1872   -0.498   0
-1.2   1   -2.50851    0.1858   -0.466   0
-1.2   1   -2.33171    0.1838   -0.429   0
-1.2   1   -2.13161   0.1811   -0.386    0
-1.2   1   -1.91021   0.1772   -0.338    0
-1.2   1   -1.66973   0.1716   -0.286    0
-1.2   1   -1.41257   0.1632   -0.231    0
-1.2   1   -1.14129   0.1504   -0.172    0
-1.2   1   -0.85861   0.1303   -0.112    0
-1.2   1   -0.56734   0.0987   -0.056    0
-1.2   1   -0.27041   0.0522   -0.014    0
-1.2   1   0.029218   0.0058   0.0002    0
-1.2   1   0.328558   0.0624   0.0205    0
-1.2   1   0.624616    0.106   0.0662    0
-1.2   1   0.914432    0.135   0.1234    0
-1.2   1   1.195111   0.1534   0.1833    0
-1.2   1    1.46385   0.1651   0.2417    0
-1.2   1   1.717962   0.1728   0.2969    0
-1.2   1   1.954909   0.1781   0.3481    0
-1.2   1   2.172323   0.1817   0.3947    0
-1.2   1   2.368032   0.1842   0.4363    0
-1.2   1    2.54008   0.1861   0.4727    0
-1.2   1   2.686749   0.1874   0.5036    0
-1.2   1   2.806572   0.1884   0.5288    0
-1.2   1   2.898353   0.1891    0.548    0
-1.2   1   2.961175   0.1895   0.5611    0
-1.2   1    2.99441   0.1897    0.568    0
-1.2   1   2.997725   0.1897   0.5687    0
-1.2   1   2.971089   0.1896   0.5632    0
-1.2   1   2.914766   0.1892   0.5514    0
-1.2   1    2.82932   0.1886   0.5335    0
-1.2   1   2.715604   0.1877   0.5097    0
-1.2   1   2.574755   0.1864      0.48   0
-1.2   1   2.408179   0.1847   0.4448    0
-1.2   1   2.217542   0.1823   0.4043    0
-1.2   1   2.004748    0.179   0.3588    0
-1.2   1   1.771923   0.1742   0.3086    0
-1.2   1   1.521394   0.1671   0.2543    0
-1.2   1   1.255663   0.1564   0.1964    0
-1.2   1   0.977387    0.1398    0.1366    0
-1.2   1   0.689344    0.1135    0.0782    0
-1.2   1   0.394414    0.0734    0.0289    0
-1.2   1   0.095543     0.019    0.0018    0
-1.2   1   -0.20428       0.04   -0.008    0
-1.2   1   -0.50207    0.0897    -0.045    0
-1.2   1   -0.79484    0.1244    -0.099    0
-1.2   1   -1.07966    0.1467    -0.158    0
-1.2   1     -1.3537   0.1609    -0.218    0
-1.2   1   -1.61421       0.17   -0.274    0
-1.2   1     -1.8586   0.1761    -0.327    0
-1.2   1   -2.08441    0.1803    -0.376    0
-1.2   1     -2.2894   0.1833      -0.42   0
-1.2   1   -2.47151    0.1854    -0.458    0
-1.2   1   -2.62893    0.1869    -0.491    0
-1.2   1   -2.76008     0.188    -0.519    0
-1.2   1   -2.86365    0.1888    -0.541    0
-1.2   1   -2.93861    0.1893    -0.556    0
-1.2   1   -2.98421    0.1896    -0.566    0
-1.2   1   -2.99999    0.1897    -0.569    0
-1.2   1     -2.9858   0.1896    -0.566    0
-1.2   1   -2.94177    0.1894    -0.557    0
-1.2   1   -2.86835    0.1889    -0.542    0
-1.2   1   -2.76627    0.1881      -0.52   0
-1.2   1   -2.63655     0.187    -0.493    0
-1.2   1   -2.48049    0.1855      -0.46   0
-1.2   1   -2.29964    0.1834    -0.422    0
-1.2   1   -2.09581    0.1805    -0.378    0
-1.2   1   -1.87105    0.1764      -0.33   0
-1.2   1   -1.62759    0.1704    -0.277    0
-1.2   1   -1.36787    0.1615    -0.221    0
-1.2   1   -1.09448    0.1477    -0.162    0
-1.2   1   -0.81015    0.1259    -0.102    0
-1.2   1   -0.51773     0.092    -0.048    0
-1.2   1   -0.22014     0.043    -0.009    0
-1.2   1   0.079653    0.0159    0.0013    0
-1.2   1    0.37865   0.0708   0.0268   0
-1.2   1   0.673864   0.1118   0.0753   0
-1.2   1   0.962344   0.1387   0.1335   0
-1.2   1   1.241209   0.1557   0.1933   0
-1.2   1   1.507672   0.1667   0.2513   0
-1.2   1   1.759071   0.1739   0.3058   0
-1.2   1   1.992894   0.1788   0.3562   0
-1.2   1   2.206805   0.1822    0.402   0
-1.2   1   2.398666   0.1846   0.4428   0
-1.2   1    2.56656   0.1864   0.4783   0
-1.2   1    2.70881   0.1876   0.5082   0
-1.2   1   2.823995   0.1885   0.5324   0
-1.2   1   2.910963   0.1892   0.5506   0
-1.2   1   2.968845   0.1895   0.5627   0
-1.2   1   2.997064   0.1897   0.5686   0
-1.2   1   2.995338   0.1897   0.5682   0
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-1.2   1   2.902415   0.1891   0.5488   0
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-1.2   1   2.693783   0.1875   0.5051   0
-1.2   1   2.548502   0.1862   0.4745   0
-1.2   1   2.377758   0.1844   0.4384   0
-1.2   1   2.183256   0.1818    0.397   0
-1.2   1   1.966939   0.1783   0.3507   0
-1.2   1    1.73097   0.1732   0.2998   0
-1.2   1   1.477705   0.1656   0.2448   0
-1.2   1   1.209675   0.1541   0.1865   0
-1.2   1   0.929559   0.1362   0.1266   0
-1.2   1   0.640155   0.1078    0.069   0
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Second derivative
                                                           ACC
            -ab^2cos(bt+c)                                 /ACC/
             1.24844051      0   0.2497     0   -1.24844    1.248
             1.51453831      0   0.3029     0   -0.99875    1.515
             1.76550335      0   0.3531     0   -0.74906    1.766
             1.99882806      0   0.3998     0   -0.49938    1.999
             2.21218115      0   0.4424     0   -0.24969    2.212
             2.40343085      0   0.4807     0          0    2.403
             2.57066626      0   0.5141   1.6   -2.69028    2.571
             2.71221643      0   0.5424   1.6   -2.15222    2.712
             2.82666702      0   0.5653   1.6   -1.61417    2.827
              2.9128745      0   0.5826   1.6   -1.07611    2.913
             2.96997749      0    0.594   1.6   -0.53806    2.97
             2.99740545      0   0.5995   1.6          0    2.997
             2.99488433      0    0.599   3.1   1.133933    2.995
             2.96243931      0   0.5925   3.1   0.907147    2.962
             2.90039458      0   0.5801   3.1    0.68036     2.9
             2.80937006      0   0.5619   3.1   0.453573    2.809
             2.69027525      0   0.5381   3.1   0.226787    2.69
              2.5443001      0   0.5089   3.1          0    2.544
             2.37290314      0   0.4746                     2.373
             2.17779691      0   0.4356                     2.178
             1.96093086      0   0.3922                     1.961
             1.72447184      0   0.3449                     1.724
             1.47078246      0   0.2942                     1.471
             1.20239752      0   0.2405                     1.202
             0.92199861      0   0.1844
              0.6323874      0   0.1265
             0.33645758      0   0.0673
             0.03716599      0   0.0074
               -0.262497     0   -0.052
-0.5595371    0   -0.112
-0.8509866    0     -0.17
-1.1339332    0   -0.227
   -1.40555   0   -0.281
  -1.663123   0   -0.333
-1.9040786    0   -0.381
-2.1260093    0   -0.425
-2.3266976    0   -0.465
-2.5041384    0   -0.501
-2.6565586    0   -0.531
-2.7824353    0   -0.556
-2.8805109    0   -0.576
-2.9498053    0     -0.59
-2.9896263    0   -0.598
-2.9995759    0      -0.6
-2.9795548    0   -0.596
-2.9297629    0   -0.586
-2.8506978    0     -0.57
-2.7431494    0   -0.549
-2.6081925    0   -0.522
-2.4471753    0   -0.489
-2.2617068    0   -0.452
   -2.05364   0   -0.411
-1.8250539    0   -0.365
-1.5782326    0   -0.316
  -1.315642   0   -0.263
  -1.039906   0   -0.208
-0.7537795    0   -0.151
-0.4601216    0   -0.092
-0.1618663    0   -0.032
0.13800638    0   0.0276
 0.4365001    0   0.0873
0.73063246    0   0.1461
1.01746458    0   0.2035
1.29413053    0   0.2588
1.55786596    0   0.3116
1.80603571    0   0.3612
2.03616014    0   0.4072
2.24593994    0   0.4492
2.43327904    0   0.4867
2.59630563    0   0.5193
2.73339079    0   0.5467
2.84316481    0   0.5686
2.92453086    0   0.5849
2.97667598    0   0.5953
2.99907913    0   0.5998
2.99151647    0   0.5983
2.95406357    0   0.5908
2.88709464    0   0.5774
2.79127882    0   0.5583
2.66757346    0   0.5335
2.51721459    0   0.5034
2.34170454    0   0.4683
2.14279696    0   0.4286
1.92247925    0   0.3845
1.68295277    0   0.3366
1.42661078    0   0.2853
1.15601457    0   0.2312
0.87386785    0   0.1748
0.58298972    0   0.1166
0.28628655    0   0.0573
-0.0132771    0   -0.003
-0.3127081    0   -0.063
-0.6090146    0   -0.122
  -0.899236   0     -0.18
-1.1804726    0   -0.236
-1.4499143    0     -0.29
-1.7048689    0   -0.341
  -1.942789   0   -0.389
-2.1612974    0   -0.432
-2.3582109    0   -0.472
-2.5315619    0   -0.506
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1.06975312
1.34422085
1.60525757
1.85025508
2.07676546
2.28252549
2.46547927
 2.6237988
 2.7559022
2.86046954
2.93645601
2.98310238
2.99994258
2.98680835
2.94383091
2.87143969
2.77035799
2.64159579
2.48643964
2.30643981
2.10339479
1.87933334
1.63649422
1.37730379
 1.1043518
0.82036548
0.52818235
0.23072179
-0.0690441
   -0.36812
-0.6635179
-0.9522861
-1.2315394
-1.4984875
-1.7504633
  -1.984949
-2.1996017
-2.3922768
  -2.561049
  -2.704232
-2.8203953
-2.9083781
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-2.9959105
-2.9653105
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-2.8158271
-2.6984373
-2.5540856
-2.3842143
-2.1905207
-1.9749401
-1.7396267
-1.4869314
-1.2193792
-0.9396434
  -0.650519
-0.3548948
-0.0557246
0.24400237
0.54129135
0.83317192
1.11672772
1.38912554
1.64764367
 1.8896991
2.11287328
2.31493633
2.49386929
2.64788434
2.77544261
2.87526957
2.94636779
2.98802687
2.99983058
2.98166097
2.93369959
2.85642566
2.75061126
2.61731366
2.45786474
2.27385764
 2.0671309
1.83975008
1.59398708
1.33229749
1.05729603
0.77173041
0.47845392
0.18039687
-0.1194626
-0.4181285
-0.7126166
-0.9999845
-1.2773608
-1.5419742
-1.7911806
-2.0224902
-2.2335917
  -2.422376
-2.5869566
-2.7256892
-2.8371877
-2.9203379
  -2.974309
-2.9985619
-2.9928541
-2.9572427
-2.8920835
-2.7980275
-2.6760146
-2.5272638
-2.3532615
-2.1557461
-1.9366913
-1.6982856
-1.4429113
-1.1731198
  -0.891607
-0.6011855
-0.3047571
-0.0052837
0.29424246
0.59082867
0.88151151
1.16338658
1.43363748
1.68956395
1.92860885
2.14838373
2.34669267
2.52155423
2.67122126
2.79419832
2.88925668
2.95544655
2.99210656
2.99887044
 2.9756706
2.92273883
2.84060403
2.73008685
2.59229155
2.42859493
2.24063258
2.03028258
1.79964667
1.55102928
1.24844051
1.24844051
1.24844051
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1.24844051
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1.24844051
         Type in required coefficients               Consider the displacement - time graph with the velocity graph
                 a      b       c                                               x =a cos(bt + c)
                 2      1       0
                             Radians

                                Displacement - time graph                                                             Velocity - time
             x




                  6                                                                                4




                                                                                             Vel
                  5
                                                                                                   3
                  4
                  3                                                                                2
                  2
                                                                                                   1
                  1
                  0                                                                                0
        -1       -1   0.57          2.14      3.71          5.28        6.85               -1           0.57        2.14            3.71   5.28
                                                                                                   -1
                 -2
                 -3                                                                                -2
                 -4
                                                                                                   -3
                 -5
                 -6                         Time t
                                                                                                   -4
                                                                                                                           Time t


Put a = 2 and b = 1.
What is the velocity with maximum displacement? Where appropriate, give answers in terms of a and b.
Where is the particle when the velocity is either maximum or minimum? Which way is the particle travelling? How do you tell?

Put b = 2. Look at the questions above again and record your results.

If the displacement is negative, the acceleration is positive. Why?
If the velocity is zero, the displacement is ….
Starting value
    0
Increment
   0.1




                 4.
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                  5
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1
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1
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1
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1
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1
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2
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2
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2
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3
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3
31
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3
32
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3
33
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3
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3
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                       45
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                       4




47.1   47.1   -1.999
47.2   47.2   -1.994
47.3   47.3   -1.969
47.4   47.4   -1.924
47.5   47.5    -1.86
47.6   47.6   -1.778
47.7   47.7   -1.677
47.8   47.8    -1.56
47.9   47.9   -1.427
48     48      -1.28
48.1   48.1    -1.12
48.2   48.2    -0.95
48.3   48.3   -0.769
48.4   48.4   -0.581
48.5   48.5   -0.387
48.6   48.6   -0.189
48.7   48.7    0.011
48.8   48.8     0.21
48.9   48.9    0.408
49     49      0.601
49.1   49.1    0.789
49.2   49.2    0.968
49.3   49.3    1.138
49.4   49.4    1.297
49.5   49.5    1.442
49.6   49.6    1.573
49.7   49.7    1.689
49.8   49.8    1.787
49.9   49.9    1.868
50     50       1.93
50.1   50.1    1.973
50.2   50.2    1.996
50.3   50.3    1.999
50.4   50.4    1.982
50.5   50.5    1.945
50.6   50.6    1.889
50.7   50.7    1.814
50.8   50.8    1.721
50.9   50.9    1.611
51     51      1.484
51.1   51.1    1.343
51.2   51.2    1.188
51.3   51.3    1.022
51.4   51.4    0.845
51.5   51.5     0.66
51.6   51.6    0.468
51.7   51.7    0.272
51.8   51.8    0.073
51.9   51.9   -0.127
52     52     -0.326
52.1   52.1   -0.521
52.2   52.2   -0.712
52.3   52.3   -0.895
52.4   52.4   -1.069
52.5   52.5   -1.232
52.6   52.6   -1.383
52.7   52.7   -1.521
52.8   52.8   -1.643
52.9   52.9   -1.748
53     53     -1.837
53.1   53.1   -1.906
53.2   53.2   -1.957
53.3   53.3   -1.989
53.4   53.4       -2
53.5   53.5   -1.991
53.6   53.6   -1.963
53.7   53.7   -1.915
53.8   53.8   -1.848
53.9   53.9   -1.762
54     54     -1.659
54.1   54.1   -1.539
54.2   54.2   -1.404
54.3   54.3   -1.254
54.4   54.4   -1.092
54.5   54.5    -0.92
54.6   54.6   -0.738
54.7   54.7   -0.549
54.8   54.8   -0.354
54.9   54.9   -0.156
55     55      0.044
55.1   55.1    0.244
55.2   55.2    0.441
55.3   55.3    0.633
55.4   55.4    0.819
55.5   55.5    0.997
55.6   55.6    1.166
55.7   55.7    1.322
55.8   55.8    1.465
55.9   55.9    1.594
56     56      1.706
56.1   56.1    1.802
56.2   56.2     1.88
56.3   56.3    1.938
56.4   56.4    1.978
56.5   56.5    1.998
56.6   56.6    1.997
56.7   56.7    1.977
56.8   56.8    1.937
56.9   56.9    1.878
57     57         1.8
57.1   57.1    1.704
57.2   57.2    1.591
57.3   57.3    1.462
57.4   57.4    1.318
57.5   57.5    1.161
57.6   57.6    0.993
57.7   57.7    0.815
57.8   57.8    0.628
57.9   57.9    0.435
58     58      0.238
58.1   58.1    0.039
58.2   58.2   -0.161
58.3   58.3   -0.359
58.4   58.4   -0.554
58.5   58.5   -0.743
58.6   58.6   -0.925
58.7   58.7   -1.097
58.8   58.8   -1.258
58.9   58.9   -1.407
59     59     -1.542
59.1   59.1   -1.662
59.2   59.2   -1.764
59.3   59.3    -1.85
59.4   59.4   -1.916
59.5   59.5   -1.964
59.6   59.6   -1.992
59.7   59.7       -2
59.8   59.8   -1.988
59.9   59.9   -1.956
60     60     -1.905
60.1   60.1   -1.834
60.2   60.2   -1.746
60.3   60.3    -1.64
60.4   60.4   -1.517
60.5   60.5   -1.379
60.6   60.6   -1.228
60.7   60.7   -1.064
60.8   60.8    -0.89
60.9   60.9   -0.707
61     61     -0.516
61.1   61.1   -0.321
61.2   61.2   -0.122
61.3   61.3    0.078
61.4   61.4    0.277
61.5   61.5    0.473
61.6   61.6    0.665
61.7   61.7     0.85
61.8   61.8    1.026
61.9   61.9    1.193
62     62      1.347
62.1   62.1    1.488
62.2   62.2    1.614
62.3   62.3    1.724
62.4   62.4    1.816
62.5   62.5    1.891
62.6   62.6    1.946
62.7   62.7    1.983
62.8   62.8    1.999
62.9   62.9    1.995
63     63      1.972
63.1   63.1    1.929
63.2   63.2    1.866
63.3   63.3    1.785
63.4   63.4    1.686
63.5   63.5     1.57
63.6   63.6    1.438
63.7   63.7    1.292
63.8   63.8    1.134
63.9   63.9    0.963
64     64      0.784
64.1   64.1    0.596
64.2   64.2    0.403
64.3   64.3    0.205
64.4   64.4    0.005
64.5   64.5   -0.194
64.6   64.6   -0.392
64.7   64.7   -0.586
64.8   64.8   -0.774
64.9   64.9   -0.954
65     65     -1.125
65.1   65.1   -1.284
65.2   65.2   -1.431
65.3   65.3   -1.563
65.4   65.4    -1.68
65.5   65.5    -1.78
65.6   65.6   -1.862
65.7   65.7   -1.926
65.8   65.8    -1.97
65.9   65.9   -1.995
66     66     -1.999
66.1   66.1   -1.984
66.2   66.2   -1.949
66.3   66.3   -1.894
66.4   66.4   -1.821
66.5   66.5   -1.729
66.6   66.6    -1.62
66.7   66.7   -1.495
66.8   66.8   -1.355
66.9   66.9   -1.201
67     67     -1.036
67.1   67.1    -0.86
67.2   67.2   -0.675
67.3   67.3   -0.484
67.4   67.4   -0.287
67.5   67.5   -0.088
67.6   67.6    0.111
67.7   67.7     0.31
67.8   67.8    0.506
67.9   67.9    0.697
68     68       0.88
68.1   68.1    1.055
68.2   68.2     1.22
68.3   68.3    1.372
68.4   68.4     1.51
68.5   68.5    1.634
68.6   68.6    1.741
68.7   68.7     1.83
68.8   68.8    1.902
68.9   68.9    1.954
69     69      1.987
69.1   69.1        2
69.2   69.2    1.993
69.3   69.3    1.966
69.4   69.4    1.919
69.5   69.5    1.854
69.6   69.6    1.769
69.7   69.7    1.667
69.8   69.8    1.549
69.9   69.9    1.415
70     70      1.267
70.1   70.1    1.106
70.2   70.2    0.934
70.3   70.3    0.753
70.4   70.4    0.564
70.5   70.5     0.37
70.6   70.6    0.171
70.7   70.7   -0.028
70.8   70.8   -0.228
70.9   70.9   -0.425
71     71     -0.618
71.1   71.1   -0.805
71.2   71.2   -0.984
71.3   71.3   -1.153
71.4   71.4    -1.31
71.5   71.5   -1.454
71.6   71.6   -1.584
71.7   71.7   -1.698
71.8   71.8   -1.795
71.9   71.9   -1.874
72     72     -1.935
72.1   72.1   -1.976
72.2   72.2   -1.997
72.3   72.3   -1.998
72.4   72.4   -1.979
72.5   72.5   -1.941
72.6   72.6   -1.883
72.7   72.7   -1.807
72.8   72.8   -1.712
72.9   72.9      -1.6
73     73     -1.472
73.1   73.1    -1.33
73.2   73.2   -1.174
73.3   73.3   -1.007
73.4   73.4   -0.829
73.5   73.5   -0.643
73.6   73.6   -0.451
73.7   73.7   -0.254
73.8   73.8   -0.055
73.9   73.9    0.145
74     74      0.343
74.1   74.1    0.538
74.2   74.2    0.728
74.3   74.3     0.91
74.4   74.4    1.084
74.5   74.5    1.246
74.6   74.6    1.396
74.7   74.7    1.532
74.8   74.8    1.653
74.9   74.9    1.757
75     75      1.844
75.1   75.1    1.912
75.2   75.2    1.961
75.3   75.3     1.99
75.4   75.4         2
75.5   75.5     1.99
75.6   75.6    1.959
75.7   75.7     1.91
75.8   75.8    1.841
75.9   75.9    1.753
76     76      1.649
76.1   76.1    1.527
76.2   76.2    1.391
76.3   76.3     1.24
76.4   76.4    1.078
76.5   76.5    0.904
76.6   76.6    0.721
76.7   76.7    0.532
76.8   76.8    0.336
76.9   76.9    0.138
77     77     -0.062
77.1   77.1   -0.261
77.2   77.2   -0.458
77.3   77.3    -0.65
77.4   77.4   -0.836
77.5   77.5   -1.013
77.6   77.6    -1.18
77.7   77.7   -1.335
77.8   77.8   -1.477
77.9   77.9   -1.604
78     78     -1.716
78.1   78.1    -1.81
78.2   78.2   -1.886
78.3   78.3   -1.943
78.4   78.4    -1.98
78.5   78.5   -1.998
78.6   78.6   -1.996
78.7   78.7   -1.974
78.8   78.8   -1.933
78.9   78.9   -1.872
79     79     -1.792
79.1   79.1   -1.694
79.2   79.2    -1.58
79.3   79.3   -1.449
79.4   79.4   -1.305
79.5   79.5   -1.147
79.6   79.6   -0.977
79.7   79.7   -0.798
79.8   79.8   -0.611
79.9   79.9   -0.418
80     80     -0.221
80.1   80.1   -0.021
80.2   80.2    0.179
80.3   80.3    0.377
80.4   80.4    0.571
80.5   80.5    0.759
80.6   80.6     0.94
80.7   80.7    1.112
80.8   80.8    1.272
80.9   80.9     1.42
81     81      1.553
81.1   81.1    1.671
81.2   81.2    1.773
81.3   81.3    1.856
81.4   81.4    1.921
81.5   81.5    1.967
81.6   81.6    1.993
81.7   81.7        2
81.8   81.8    1.986
81.9   81.9    1.952
82     82      1.899
82.1   82.1    1.827
82.2   82.2    1.737
82.3   82.3    1.629
82.4   82.4    1.505
82.5   82.5    1.367
82.6   82.6    1.214
82.7   82.7    1.049
82.8   82.8    0.874
82.9   82.9     0.69
83     83      0.499
83.1   83.1    0.303
83.2   83.2    0.104
83.3   83.3   -0.096
83.4   83.4   -0.295
83.5   83.5   -0.491
83.6   83.6   -0.682
83.7   83.7   -0.866
83.8   83.8   -1.042
83.9   83.9   -1.207
84     84      -1.36
84.1   84.1      -1.5
84.2   84.2   -1.624
84.3   84.3   -1.733
84.4   84.4   -1.824
84.5   84.5   -1.897
84.6   84.6    -1.95
84.7   84.7   -1.985
84.8   84.8   -1.999
84.9   84.9   -1.994
85     85     -1.969
85.1   85.1   -1.924
85.2   85.2    -1.86
85.3   85.3   -1.777
85.4   85.4   -1.676
85.5   85.5   -1.559
85.6   85.6   -1.426
85.7   85.7   -1.279
85.8   85.8   -1.119
85.9   85.9   -0.948
86     86     -0.767
86.1   86.1   -0.579
86.2   86.2   -0.385
86.3   86.3   -0.187
86.4   86.4    0.012
86.5   86.5    0.212
86.6   86.6    0.409
86.7   86.7    0.603
86.8   86.8     0.79
86.9   86.9     0.97
87     87       1.14
87.1   87.1    1.298
87.2   87.2    1.443
87.3   87.3    1.574
87.4   87.4     1.69
87.5   87.5    1.788
87.6   87.6    1.869
87.7   87.7     1.93
87.8   87.8    1.973
87.9   87.9    1.996
88     88      1.999
88.1   88.1    1.982
88.2   88.2    1.945
88.3   88.3    1.889
88.4   88.4    1.813
88.5   88.5     1.72
88.6   88.6     1.61
88.7   88.7    1.483
88.8   88.8    1.342
88.9   88.9    1.187
89     89       1.02
89.1   89.1    0.844
89.2   89.2    0.658
89.3   89.3    0.466
89.4   89.4     0.27
89.5   89.5    0.071
89.6   89.6   -0.129
89.7   89.7   -0.328
89.8   89.8   -0.523
89.9   89.9   -0.713
90     90     -0.896
90.1   90.1    -1.07
90.2   90.2   -1.234
90.3   90.3   -1.385
90.4   90.4   -1.522
90.5   90.5   -1.644
90.6   90.6   -1.749
90.7   90.7   -1.837
90.8   90.8   -1.907
90.9   90.9   -1.958
91     91     -1.989
91.1   91.1       -2
91.2   91.2   -1.991
91.3   91.3   -1.963
91.4   91.4   -1.914
91.5   91.5   -1.847
91.6   91.6   -1.761
91.7   91.7   -1.658
91.8   91.8   -1.538
91.9   91.9   -1.402
92     92     -1.253
92.1   92.1   -1.091
92.2   92.2   -0.918
92.3   92.3   -0.736
92.4   92.4   -0.547
92.5   92.5   -0.352
92.6   92.6   -0.154
92.7   92.7    0.046
92.8   92.8    0.245
92.9   92.9    0.442
93     93      0.635
93.1   93.1    0.821
93.2   93.2    0.999
93.3   93.3    1.167
93.4   93.4    1.323
93.5   93.5    1.466
93.6   93.6    1.595
93.7   93.7    1.707
93.8   93.8    1.803
93.9   93.9     1.88
94     94      1.939
94.1   94.1    1.978
94.2   94.2    1.998
94.3   94.3    1.997
94.4   94.4    1.977
94.5   94.5    1.937
94.6   94.6    1.877
94.7   94.7    1.799
94.8   94.8    1.703
94.9   94.9    1.589
95     95       1.46
95.1   95.1    1.317
95.2   95.2     1.16
95.3   95.3    0.991
95.4   95.4    0.813
95.5   95.5    0.626
95.6   95.6    0.434
95.7   95.7    0.237
95.8   95.8    0.037
95.9   95.9   -0.163
96     96     -0.361
96.1   96.1   -0.555
96.2   96.2   -0.744
96.3   96.3   -0.926
96.4   96.4   -1.098
96.5   96.5    -1.26
96.6   96.6   -1.409
96.7   96.7   -1.543
96.8   96.8   -1.663
96.9   96.9   -1.765
97     97      -1.85
97.1   97.1   -1.917
97.2   97.2   -1.964
97.3    97.3    -1.992
97.4    97.4        -2
97.5    97.5    -1.988
97.6    97.6    -1.956
97.7    97.7    -1.904
97.8    97.8    -1.834
97.9    97.9    -1.745
 98      98     -1.639
98.1    98.1    -1.516
98.2    98.2    -1.378
98.3    98.3    -1.227
98.4    98.4    -1.063
98.5    98.5    -0.888
98.6    98.6    -0.705
98.7    98.7    -0.514
98.8    98.8    -0.319
98.9    98.9     -0.12
 99      99       0.08
99.1    99.1     0.279
99.2    99.2     0.475
99.3    99.3     0.667
99.4    99.4     0.852
99.5    99.5     1.028
99.6    99.6     1.194
99.7    99.7     1.348
99.8    99.8     1.489
99.9    99.9     1.615
100     100      1.725
100.1   100.1    1.817
100.2   100.2    1.891
100.3   100.3    1.947
100.4   100.4    1.983
100.5   100.5    1.999
100.6   100.6    1.995
100.7   100.7    1.971
100.8   100.8    1.928
100.9   100.9    1.865
101     101      1.784
101.1   101.1    1.685
101.2   101.2    1.569
101.3   101.3    1.437
101.4   101.4    1.291
101.5   101.5    1.132
101.6   101.6    0.962
101.7   101.7    0.782
101.8   101.8    0.594
101.9   101.9    0.401
102     102      0.203
102.1   102.1    0.004
102.2   102.2   -0.196
102.3   102.3   -0.394
102.4   102.4   -0.588
102.5   102.5   -0.776
102.6   102.6   -0.956
102.7   102.7   -1.126
102.8   102.8   -1.286
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               t    x      y             Velocity

                    t     a cos(bt+c)     vectors     Speed
              0     0         2                     | velocity |                                                                     Second derivative
              0.1   0.1   1.99             1.00                  Derivative                        velocity vectors         speed
              0.2   0.2   1.96             0.00            1              1 -ab sin(bt+c)                                   \vel\              0
              0.3   0.3   1.91                                            1           0 0.2      0           0          2      1               0
              0.4   0.4   1.84              1.00                          1 -0.19967 0.2      -0.4         0.2          2    1.02              0
              0.5   0.5   1.76             -0.20         1.02             1 -0.39734 0.2 0.0233            0.4          2    1.076             0
              0.6   0.6   1.65                                            1 -0.59104 0.2 -0.118            0.6          2    1.162             0
              0.7   0.7   1.53              1.00                          1 -0.77884 0.2 -0.156            0.8          2    1.268             0
              0.8   0.8   1.39             -0.40        1.076             1 -0.95885 0.2 -0.192              1          2    1.385             0
              0.9   0.9   1.24                                            1 -1.12928 0.2 -0.226            1.6    -0.0584    1.508             0
              1     1     1.08                                            1 -1.28844 0.2 -0.258            1.8 -0.45823      1.631             0
5.28   6.85   1.1   1.1   0.91          Acceleration| acceleration |      1 -1.43471 0.2 -0.287              2 -0.85806      1.749             0
              1.2   1.2   0.72            vectors                         1 -1.56665 0.2 -0.313            2.2 -1.25789      1.859             0
              1.3   1.3   0.53                                            1 -1.68294 0.2 -0.337            2.4 -1.65772      1.958             0
              1.4   1.4   0.34              0.00                          1 -1.78241 0.2 -0.356            2.6 -2.05755      2.044             0
              1.5   1.5   0.14             -2.00           2              1 -1.86408 0.2 -0.373            3.2 -1.99659      2.115             0
              1.6   1.6    -0.1                                           1 -1.92712 0.2 -0.385            3.4 -1.97324      2.171             0
              1.7   1.7    -0.3             0.00                          1    -1.9709 0.2 -0.394          3.6 -1.94989      2.21              0
              1.8   1.8    -0.5            -1.99         1.99             1 -1.99499 0.2 -0.399            3.8 -1.92654      2.232             0
              1.9   1.9    -0.6                                           1 -1.99915 0.2      -0.4           4 -1.90319      2.235             0
              2     2      -0.8                                           1 -1.98333 0.2 -0.397              4 -1.90319      2.221             0
              2.1   2.1      -1             0.00                          1    -1.9477 0.2  -0.39            4 -1.90319      2.189             0
              2.2   2.2    -1.2            -1.96         1.96             1    -1.8926 0.2 -0.379                            2.141             0
              2.3   2.3    -1.3                                           1 -1.81859 0.2 -0.364                              2.075             0
              2.4   2.4    -1.5                                           1 -1.72642 0.2 -0.345                              1.995             0
              2.5   2.5    -1.6                                           1 -1.61699 0.2 -0.323                              1.901             0
              2.6   2.6    -1.7                                           1 -1.49141 0.2 -0.298                              1.796             0
              2.7   2.7    -1.8                                           1 -1.35093 0.2    -0.27                            1.681             0
              2.8   2.8    -1.9                                           1 -1.19694 0.2 -0.239                                                0
              2.9   2.9    -1.9                                           1     -1.031 0.2 -0.206                                              0
              3     3        -2                                           1 -0.85476 0.2 -0.171                                                0
3.1   3.1     -2   1   -0.66998    0.2   -0.134    0
3.2   3.2     -2   1     -0.4785   0.2   -0.096    0
3.3   3.3     -2   1   -0.28224    0.2   -0.056    0
3.4   3.4   -1.9   1   -0.08316    0.2   -0.017    0
3.5   3.5   -1.9   1   0.116748    0.2   0.0233    0
3.6   3.6   -1.8   1   0.315491    0.2   0.0631    0
3.7   3.7   -1.7   1   0.511082    0.2   0.1022    0
3.8   3.8   -1.6   1   0.701566    0.2   0.1403    0
3.9   3.9   -1.5   1   0.885041    0.2    0.177    0
4     4     -1.3   1   1.059672    0.2   0.2119    0
4.1   4.1   -1.1   1   1.223716    0.2   0.2447    0
4.2   4.2     -1   1   1.375532    0.2   0.2751    0
4.3   4.3   -0.8   1   1.513605    0.2   0.3027    0
4.4   4.4   -0.6   1   1.636554    0.2   0.3273    0
4.5   4.5   -0.4   1   1.743152    0.2   0.3486    0
4.6   4.6   -0.2   1   1.832332    0.2   0.3665    0
4.7   4.7     -0   1   1.903204    0.2   0.3806    0
4.8   4.8   0.17   1    1.95506    0.2    0.391    0
4.9   4.9   0.37   1   1.987382    0.2   0.3975    0
5     5     0.57   1   1.999847    0.2       0.4   0
5.1   5.1   0.76   1   1.992329    0.2   0.3985    0
5.2   5.2   0.94   1   1.964905    0.2    0.393    0
5.3   5.3   1.11   1   1.917849    0.2   0.3836    0
5.4   5.4   1.27   1   1.851629    0.2   0.3703    0
5.5   5.5   1.42   1   1.766909    0.2   0.3534    0
5.6   5.6   1.55   1   1.664535    0.2   0.3329    0
5.7   5.7   1.67   1   1.545529    0.2   0.3091    0
5.8   5.8   1.77   1   1.411081    0.2   0.2822    0
5.9   5.9   1.85   1   1.262533    0.2   0.2525    0
6     6     1.92   1   1.101371    0.2   0.2203    0
6.1   6.1   1.97   1   0.929204    0.2   0.1858    0
6.2   6.2   1.99   1   0.747753    0.2   0.1496    0
6.3   6.3      2   1   0.558831    0.2   0.1118    0
6.4   6.4   1.99   1   0.364325    0.2   0.0729    0
6.5   6.5   1.95   1   0.166179    0.2   0.0332    0
6.6   6.6    1.9   1 -0.03363 0.2 -0.007     0
6.7   6.7   1.83   1   -0.2331 0.2 -0.047    0
6.8   6.8   1.74   1 -0.43024 0.2 -0.086     0
6.9   6.9   1.63   1 -0.62308 0.2 -0.125     0
7     7     1.51   1   -0.8097 0.2 -0.162    0
7.1   7.1   1.37   1 -0.98823 0.2 -0.198     0
7.2   7.2   1.22   1 -1.15688 0.2 -0.231     0
7.3   7.3   1.05   1 -1.31397 0.2 -0.263     0
7.4   7.4   0.88   1 -1.45794 0.2 -0.292     0
7.5   7.5   0.69   1 -1.58734 0.2 -0.317     0
7.6   7.6    0.5   1 -1.70087 0.2   -0.34    0
7.7   7.7   0.31   1 -1.79742 0.2 -0.359     0
7.8   7.8   0.11   1    -1.876 0.2 -0.375    0
7.9   7.9   -0.1   1 -1.93584 0.2 -0.387     0
8     8     -0.3   1 -1.97634 0.2 -0.395     0
8.1   8.1   -0.5   1 -1.99709 0.2 -0.399     0
8.2   8.2   -0.7   1 -1.99788 0.2     -0.4   0
8.3   8.3   -0.9   1 -1.97872 0.2 -0.396     0
8.4   8.4     -1   1 -1.93978 0.2 -0.388     0
8.5   8.5   -1.2   1 -1.88146 0.2 -0.376     0
8.6   8.6   -1.4   1 -1.80434 0.2 -0.361     0
8.7   8.7   -1.5   1   -1.7092 0.2 -0.342    0
8.8   8.8   -1.6   1 -1.59697 0.2 -0.319     0
8.9   8.9   -1.7   1 -1.46879 0.2 -0.294     0
9     9     -1.8   1 -1.32594 0.2 -0.265     0
9.1   9.1   -1.9   1 -1.16983 0.2 -0.234     0
9.2   9.2   -1.9   1 -1.00204 0.2     -0.2   0
9.3   9.3     -2   1 -0.82424 0.2 -0.165     0
9.4   9.4     -2   1   -0.6382 0.2 -0.128    0
9.5   9.5     -2   1 -0.44578 0.2 -0.089     0
9.6   9.6     -2   1 -0.24891 0.2   -0.05    0
9.7   9.7   -1.9   1 -0.04955 0.2   -0.01    0
9.8   9.8   -1.9   1 0.150302 0.2 0.0301     0
9.9   9.9   -1.8   1 0.348654 0.2 0.0697     0
10    10    -1.7   1 0.543521 0.2 0.1087     0
10.1   10.1   -1.6   1   0.732958   0.2   0.1466    0
10.2   10.2   -1.4   1   0.915072   0.2    0.183    0
10.3   10.3   -1.3   1   1.088042   0.2   0.2176    0
10.4   10.4   -1.1   1   1.250141   0.2      0.25   0
10.5   10.5     -1   1   1.399749   0.2   0.2799    0
10.6   10.6   -0.8   1   1.535372   0.2   0.3071    0
10.7   10.7   -0.6   1   1.655653   0.2   0.3311    0
10.8   10.8   -0.4   1   1.759392   0.2   0.3519    0
10.9   10.9   -0.2   1   1.845551   0.2   0.3691    0
11     11     0.01   1    1.91327   0.2   0.3827    0
11.1   11.1   0.21   1   1.961872   0.2   0.3924    0
11.2   11.2   0.41   1   1.990873   0.2   0.3982    0
11.3   11.3    0.6   1    1.99998   0.2       0.4   0
11.4   11.4   0.79   1   1.989105   0.2   0.3978    0
11.5   11.5   0.97   1   1.958355   0.2   0.3917    0
11.6   11.6   1.14   1   1.908038   0.2   0.3816    0
11.7   11.7    1.3   1   1.838657   0.2   0.3677    0
11.8   11.8   1.44   1   1.750904   0.2   0.3502    0
11.9   11.9   1.57   1   1.645657   0.2   0.3291    0
12     12     1.69   1   1.523967   0.2   0.3048    0
12.1   12.1   1.79   1    1.38705   0.2   0.2774    0
12.2   12.2   1.87   1   1.236274   0.2   0.2473    0
12.3   12.3   1.93   1   1.073146   0.2   0.2146    0
12.4   12.4   1.97   1   0.899295   0.2   0.1799    0
12.5   12.5      2   1   0.716459   0.2   0.1433    0
12.6   12.6      2   1   0.526464   0.2   0.1053    0
12.7   12.7   1.98   1   0.331208   0.2   0.0662    0
12.8   12.8   1.95   1   0.132644   0.2   0.0265    0
12.9   12.9   1.89   1   -0.06725   0.2   -0.013    0
13     13     1.81   1   -0.26646   0.2   -0.053    0
13.1   13.1   1.72   1   -0.46302   0.2   -0.093    0
13.2   13.2   1.61   1   -0.65495   0.2   -0.131    0
13.3   13.3   1.49   1   -0.84033   0.2   -0.168    0
13.4   13.4   1.34   1   -1.01732   0.2   -0.203    0
13.5   13.5   1.19   1   -1.18415   0.2   -0.237    0
13.6   13.6   1.02   1   -1.33914    0.2   -0.268    0
13.7   13.7   0.85   1   -1.48075    0.2   -0.296    0
13.8   13.8   0.66   1   -1.60757    0.2   -0.322    0
13.9   13.9   0.47   1   -1.71832    0.2   -0.344    0
14     14     0.27   1   -1.81191    0.2   -0.362    0
14.1   14.1   0.07   1   -1.88739    0.2   -0.377    0
14.2   14.2   -0.1   1   -1.94402    0.2   -0.389    0
14.3   14.3   -0.3   1   -1.98121    0.2   -0.396    0
14.4   14.4   -0.5   1   -1.99862    0.2      -0.4   0
14.5   14.5   -0.7   1   -1.99605    0.2   -0.399    0
14.6   14.6   -0.9   1   -1.97354    0.2   -0.395    0
14.7   14.7   -1.1   1   -1.93132    0.2   -0.386    0
14.8   14.8   -1.2   1   -1.86979    0.2   -0.374    0
14.9   14.9   -1.4   1   -1.78958    0.2   -0.358    0
15     15     -1.5   1   -1.69149    0.2   -0.338    0
15.1   15.1   -1.6   1     -1.5765   0.2   -0.315    0
15.2   15.2   -1.7   1   -1.44576    0.2   -0.289    0
15.3   15.3   -1.8   1   -1.30058    0.2     -0.26   0
15.4   15.4   -1.9   1   -1.14239    0.2   -0.228    0
15.5   15.5     -2   1     -0.9728   0.2   -0.195    0
15.6   15.6     -2   1   -0.79348    0.2   -0.159    0
15.7   15.7     -2   1   -0.60624    0.2   -0.121    0
15.8   15.8     -2   1   -0.41293    0.2   -0.083    0
15.9   15.9     -2   1   -0.21551    0.2   -0.043    0
16     16     -1.9   1   -0.01593    0.2   -0.003    0
16.1   16.1   -1.8   1   0.183814    0.2   0.0368    0
16.2   16.2   -1.8   1   0.381717    0.2   0.0763    0
16.3   16.3   -1.7   1   0.575807    0.2   0.1152    0
16.4   16.4   -1.5   1   0.764143    0.2   0.1528    0
16.5   16.5   -1.4   1   0.944844    0.2    0.189    0
16.6   16.6   -1.3   1   1.116105    0.2   0.2232    0
16.7   16.7   -1.1   1   1.276213    0.2   0.2552    0
16.8   16.8   -0.9   1   1.423571    0.2   0.2847    0
16.9   16.9   -0.7   1   1.556704    0.2   0.3113    0
17     17     -0.6   1   1.674284    0.2   0.3349    0
17.1   17.1   -0.4   1   1.775134    0.2    0.355    0
17.2   17.2   -0.2   1   1.858248    0.2   0.3716    0
17.3   17.3   0.04   1   1.922795    0.2   0.3846    0
17.4   17.4   0.24   1    1.96813    0.2   0.3936    0
17.5   17.5   0.44   1      1.9938   0.2   0.3988    0
17.6   17.6   0.63   1   1.999549    0.2   0.3999    0
17.7   17.7   0.82   1   1.985319    0.2   0.3971    0
17.8   17.8      1   1   1.951252    0.2   0.3903    0
17.9   17.9   1.16   1   1.897689    0.2   0.3795    0
18     18     1.32   1   1.825165    0.2    0.365    0
18.1   18.1   1.46   1   1.734404    0.2   0.3469    0
18.2   18.2   1.59   1   1.626314    0.2   0.3253    0
18.3   18.3   1.71   1   1.501974    0.2   0.3004    0
18.4   18.4    1.8   1   1.362628    0.2   0.2725    0
18.5   18.5   1.88   1   1.209666    0.2   0.2419    0
18.6   18.6   1.94   1   1.044617    0.2   0.2089    0
18.7   18.7   1.98   1   0.869131    0.2   0.1738    0
18.8   18.8      2   1   0.684961    0.2    0.137    0
18.9   18.9      2   1   0.493947    0.2   0.0988    0
19     19     1.98   1   0.297998    0.2   0.0596    0
19.1   19.1   1.94   1   0.099071    0.2   0.0198    0
19.2   19.2   1.88   1   -0.10085    0.2     -0.02   0
19.3   19.3    1.8   1   -0.29975    0.2     -0.06   0
19.4   19.4    1.7   1   -0.49567    0.2   -0.099    0
19.5   19.5   1.59   1   -0.68663    0.2   -0.137    0
19.6   19.6   1.46   1   -0.87073                    0
19.7   19.7   1.32   1   -1.04613                    0
19.8   19.8   1.16   1   -1.21108                    0
19.9   19.9   0.99   1   -1.36393                    0
20     20     0.82   1   -1.50315                    0
20.1   20.1   0.63   1   -1.62735                    0
20.2   20.2   0.44   1   -1.73529                    0
20.3   20.3   0.24   1   -1.82589                    0
20.4   20.4   0.04   1   -1.89825                    0
20.5   20.5   -0.2   1   -1.95164                    0
20.6   20.6   -0.4   1   -1.98553    0
20.7   20.7   -0.6   1   -1.99959    0
20.8   20.8   -0.7   1   -1.99366    0
20.9   20.9   -0.9   1   -1.96781    0
21     21     -1.1   1   -1.92231    0
21.1   21.1   -1.3   1   -1.85759    0
21.2   21.2   -1.4   1   -1.77432    0
21.3   21.3   -1.5   1   -1.67331    0
21.4   21.4   -1.7   1   -1.55559    0
21.5   21.5   -1.8   1   -1.42232    0
21.6   21.6   -1.8   1   -1.27485    0
21.7   21.7   -1.9   1   -1.11463    0
21.8   21.8     -2   1   -0.94328    0
21.9   21.9     -2   1     -0.7625   0
22     22       -2   1   -0.57411    0
22.1   22.1     -2   1   -0.37997    0
22.2   22.2     -2   1   -0.18204    0
22.3   22.3   -1.9   1   0.017703    0
22.4   22.4   -1.8   1   0.217273    0
22.5   22.5   -1.7   1   0.414673    0
22.6   22.6   -1.6   1   0.607929    0
22.7   22.7   -1.5   1   0.795111    0
22.8   22.8   -1.4   1   0.974349    0
22.9   22.9   -1.2   1   1.143851    0
23     23     -1.1   1   1.301925    0
23.1   23.1   -0.9   1    1.44699    0
23.2   23.2   -0.7   1   1.577597    0
23.3   23.3   -0.5   1   1.692441    0
23.4   23.4   -0.3   1   1.790375    0
23.5   23.5   -0.1   1    1.87042    0
23.6   23.6   0.08   1   1.931776    0
23.7   23.7   0.28   1   1.973831    0
23.8   23.8   0.47   1   1.996164    0
23.9   23.9   0.66   1   1.998552    0
24     24     0.85   1   1.980971    0
24.1   24.1   1.02   1   1.943597    0
24.2   24.2   1.19   1   1.886803    0
24.3   24.3   1.35   1   1.811157    0
24.4   24.4   1.49   1   1.717414    0
24.5   24.5   1.61   1   1.606511    0
24.6   24.6   1.72   1   1.479557    0
24.7   24.7   1.82   1    1.33782    0
24.8   24.8   1.89   1   1.182715    0
24.9   24.9   1.95   1   1.015793    0
25     25     1.98   1   0.838722    0
25.1   25.1      2   1    0.65327    0
25.2   25.2      2   1   0.461291    0
25.3   25.3   1.97   1   0.264704    0
25.4   25.4   1.93   1   0.065471    0
25.5   25.5   1.87   1   -0.13442    0
25.6   25.6   1.79   1   -0.33296    0
25.7   25.7   1.69   1   -0.52818    0
25.8   25.8   1.57   1   -0.71812    0
25.9   25.9   1.44   1   -0.90088    0
26     26     1.29   1   -1.07464    0
26.1   26.1   1.14   1   -1.23767    0
26.2   26.2   0.97   1   -1.38833    0
26.3   26.3   0.79   1   -1.52512    0
26.4   26.4    0.6   1   -1.64667    0
26.5   26.5    0.4   1   -1.75176    0
26.6   26.6   0.21   1   -1.83936    0
26.7   26.7   0.01   1   -1.90857    0
26.8   26.8   -0.2   1   -1.95872    0
26.9   26.9   -0.4   1   -1.98929    0
27     27     -0.6   1   -1.99999    0
27.1   27.1   -0.8   1     -1.9907   0
27.2   27.2     -1   1   -1.96153    0
27.3   27.3   -1.1   1   -1.91275    0
27.4   27.4   -1.3   1   -1.84487    0
27.5   27.5   -1.4   1   -1.75855    0
27.6   27.6   -1.6   1   -1.65466    0
27.7   27.7   -1.7   1   -1.53423    0
27.8   27.8   -1.8   1   -1.39848    0
27.9   27.9   -1.9   1   -1.24875    0
28     28     -1.9   1   -1.08655    0
28.1   28.1     -2   1   -0.91349    0
28.2   28.2     -2   1   -0.73131    0
28.3   28.3     -2   1   -0.54181    0
28.4   28.4     -2   1     -0.3469   0
28.5   28.5   -1.9   1   -0.14853    0
28.6   28.6   -1.9   1   0.051327    0
28.7   28.7   -1.8   1   0.250671    0
28.8   28.8   -1.7   1   0.447511    0
28.9   28.9   -1.6   1    0.63988    0
29     29     -1.5   1   0.825855    0
29.1   29.1   -1.4   1   1.003579    0
29.2   29.2   -1.2   1   1.171275    0
29.3   29.3     -1   1   1.327268    0
29.4   29.4   -0.9   1   1.469999    0
29.5   29.5   -0.7   1   1.598043    0
29.6   29.6   -0.5   1    1.71012    0
29.7   29.7   -0.3   1   1.805109    0
29.8   29.8   -0.1   1   1.882063    0
29.9   29.9   0.11   1   1.940211    0
30     30     0.31   1   1.978974    0
30.1   30.1    0.5   1   1.997964    0
30.2   30.2   0.69   1    1.99699    0
30.3   30.3   0.88   1   1.976063    0
30.4   30.4   1.05   1   1.935392    0
30.5   30.5   1.22   1   1.875383    0
30.6   30.6   1.37   1   1.796636    0
30.7   30.7   1.51   1   1.699938    0
30.8   30.8   1.63   1   1.586254    0
30.9   30.9   1.74   1   1.456722    0
31     31     1.83   1   1.312634    0
31.1   31.1    1.9   1    1.15543    0
31.2   31.2   1.95   1   0.986682    0
31.3   31.3   1.99   1   0.808075    0
31.4   31.4      2   1   0.621395    0
31.5   31.5   1.99   1   0.428505    0
31.6   31.6   1.97   1   0.231334    0
31.7   31.7   1.92   1   0.031852    0
31.8   31.8   1.85   1   -0.16795    0
31.9   31.9   1.77   1   -0.36607    0
32     32     1.67   1   -0.56054    0
32.1   32.1   1.55   1     -0.7494   0
32.2   32.2   1.42   1   -0.93078    0
32.3   32.3   1.27   1   -1.10285    0
32.4   32.4   1.11   1   -1.26391    0
32.5   32.5   0.94   1   -1.41234    0
32.6   32.6   0.75   1   -1.54666    0
32.7   32.7   0.57   1   -1.66552    0
32.8   32.8   0.37   1   -1.76774    0
32.9   32.9   0.17   1     -1.8523   0
33     33       -0   1   -1.91835    0
33.1   33.1   -0.2   1   -1.96524    0
33.2   33.2   -0.4   1   -1.99248    0
33.3   33.3   -0.6   1   -1.99982    0
33.4   33.4   -0.8   1   -1.98718    0
33.5   33.5     -1   1   -1.95469    0
33.6   33.6   -1.2   1   -1.90266    0
33.7   33.7   -1.3   1   -1.83162    0
33.8   33.8   -1.5   1   -1.74228    0
33.9   33.9   -1.6   1   -1.63553    0
34     34     -1.7   1   -1.51244    0
34.1   34.1   -1.8   1   -1.37424    0
34.2   34.2   -1.9   1   -1.22231    0
34.3   34.3   -1.9   1   -1.05817    0
34.4   34.4     -2   1   -0.88345    0
34.5   34.5     -2   1     -0.6999   0
34.6   34.6     -2   1   -0.50936    0
34.7   34.7     -2   1   -0.31374    0
34.8   34.8   -1.9   1   -0.11497    0
34.9   34.9   -1.9   1   0.084936    0
35     35     -1.8   1   0.283998    0
35.1   35.1   -1.7   1   0.480223    0
35.2   35.2   -1.6   1    0.67165    0
35.3   35.3   -1.5   1   0.856365    0
35.4   35.4   -1.3   1   1.032524    0
35.5   35.5   -1.2   1   1.198367    0
35.6   35.6     -1   1   1.352236    0
35.7   35.7   -0.8   1   1.492593    0
35.8   35.8   -0.6   1   1.618038    0
35.9   35.9   -0.5   1   1.727315    0
36     36     -0.3   1   1.819333    0
36.1   36.1   -0.1   1   1.893174    0
36.2   36.2   0.14   1   1.948098    0
36.3   36.3   0.34   1   1.983558    0
36.4   36.4   0.54   1   1.999198    0
36.5   36.5   0.73   1   1.994864    0
36.6   36.6   0.91   1   1.970597    0
36.7   36.7   1.08   1    1.92664    0
36.8   36.8   1.24   1   1.863434    0
36.9   36.9   1.39   1   1.781608    0
37     37     1.53   1   1.681982    0
37.1   37.1   1.65   1   1.565549    0
37.2   37.2   1.76   1   1.433474    0
37.3   37.3   1.84   1   1.287076    0
37.4   37.4   1.91   1   1.127818    0
37.5   37.5   1.96   1   0.957292    0
37.6   37.6   1.99   1      0.7772   0
37.7   37.7      2   1   0.589343    0
37.8   37.8   1.99   1   0.395598    0
37.9   37.9   1.96   1   0.197899    0
38     38     1.91   1   -0.00178    0
38.1   38.1   1.84   1 -0.20143    0
38.2   38.2   1.75   1 -0.39908    0
38.3   38.3   1.65   1 -0.59274    0
38.4   38.4   1.53   1 -0.78047    0
38.5   38.5   1.39   1 -0.96041    0
38.6   38.6   1.24   1 -1.13075    0
38.7   38.7   1.08   1 -1.28979    0
38.8   38.8   0.91   1 -1.43595    0
38.9   38.9   0.72   1 -1.56776    0
39     39     0.53   1   -1.6839   0
39.1   39.1   0.34   1 -1.78322    0
39.2   39.2   0.14   1 -1.86472    0
39.3   39.3   -0.1   1 -1.92759    0
39.4   39.4   -0.3   1   -1.9712   0
39.5   39.5   -0.5   1 -1.99511    0
39.6   39.6   -0.6   1 -1.99909    0
39.7   39.7   -0.8   1   -1.9831   0
39.8   39.8     -1   1 -1.94729    0
39.9   39.9   -1.2   1 -1.89203    0
40     40     -1.3   1 -1.81785    0
40.1   40.1   -1.5   1 -1.72552    0
40.2   40.2   -1.6   1 -1.61595    0
40.3   40.3   -1.7   1 -1.49023    0
40.4   40.4   -1.8   1 -1.34962    0
40.5   40.5   -1.9   1 -1.19552    0
40.6   40.6   -1.9   1 -1.02948    0
40.7   40.7     -2   1 -0.85315    0
40.8   40.8     -2   1   -0.6683   0
40.9   40.9     -2   1 -0.47677    0
41     41       -2   1 -0.28048    0
41.1   41.1   -1.9   1 -0.08139    0
41.2   41.2   -1.9   1 0.118522    0
41.3   41.3   -1.8   1 0.317245    0
41.4   41.4   -1.7   1 0.512799    0
41.5   41.5   -1.6   1 0.70323     0
41.6   41.6   -1.5   1   0.886633    0
41.7   41.7   -1.3   1   1.061178    0
41.8   41.8   -1.1   1    1.22512    0
41.9   41.9     -1   1   1.376821    0
42     42     -0.8   1   1.514765    0
42.1   42.1   -0.6   1   1.637575    0
42.2   42.2   -0.4   1   1.744022    0
42.3   42.3   -0.2   1   1.833043    0
42.4   42.4     -0   1   1.903749    0
42.5   42.5   0.18   1   1.955434    0
42.6   42.6   0.37   1    1.98758    0
42.7   42.7   0.57   1   1.999868    0
42.8   42.8   0.76   1   1.992173    0
42.9   42.9   0.94   1   1.964573    0
43     43     1.11   1   1.917344    0
43.1   43.1   1.27   1   1.850957    0
43.2   43.2   1.42   1   1.766076    0
43.3   43.3   1.55   1   1.663549    0
43.4   43.4   1.67   1   1.544401    0
43.5   43.5   1.77   1   1.409821    0
43.6   43.6   1.86   1   1.261155    0
43.7   43.7   1.92   1   1.099888    0
43.8   43.8   1.97   1   0.927631    0
43.9   43.9   1.99   1   0.746106    0
44     44        2   1   0.557125    0
44.1   44.1   1.99   1   0.362578    0
44.2   44.2   1.95   1   0.164409    0
44.3   44.3    1.9   1     -0.0354   0
44.4   44.4   1.83   1   -0.23486    0
44.5   44.5   1.74   1   -0.43197    0
44.6   44.6   1.63   1   -0.62477    0
44.7   44.7   1.51   1   -0.81132    0
44.8   44.8   1.37   1   -0.98977    0
44.9   44.9   1.22   1   -1.15833    0
45     45     1.05   1   -1.31531    0
45.1   45.1   0.88   1   -1.45915    0
45.2   45.2   0.69   1   -1.58842    0
45.3   45.3    0.5   1   -1.70181    0
45.4   45.4    0.3   1   -1.79819    0
45.5   45.5   0.11   1   -1.87661    0
45.6   45.6   -0.1   1   -1.93628    0
45.7   45.7   -0.3   1   -1.97661    0
45.8   45.8   -0.5   1   -1.99718    0
45.9   45.9   -0.7   1     -1.9978   0
46     46     -0.9   1   -1.97846    0
46.1   46.1     -1   1   -1.93935    0
46.2   46.2   -1.2   1   -1.88086    0
46.3   46.3   -1.4   1   -1.80358    0
46.4   46.4   -1.5   1   -1.70827    0
46.5   46.5   -1.6   1     -1.5959   0
46.6   46.6   -1.7   1   -1.46759    0
46.7   46.7   -1.8   1   -1.32461    0
46.8   46.8   -1.9   1   -1.16839    0
46.9   46.9     -2   1     -1.0005   0
47     47       -2   1   -0.82262    0
                 2   1   -0.63651    0
                 2   1   -0.44405    0
                 2   1   -0.24715    0
                 2   1   -0.04778    0
                 2   1   0.152073    0
                 2   1   0.350403    0
                 2   1   0.545231    0
                 2   1   0.734611    0
                 2   1   0.916651    0
                 2   1   1.089532    0
                 2   1   1.251527    0
                 2   1   1.401018    0
                 2   1   1.536509    0
                 2   1   1.656649    0
                 2   1   1.760236    0
2   1   1.846235    0
2   1   1.913787    0
2   1   1.962217    0
2   1   1.991041    0
2   1   1.999972    0
2   1   1.988919    0
2   1   1.957994    0
2   1   1.907505    0
2   1   1.837957    0
2   1   1.750045    0
2   1   1.644647    0
2   1   1.522816    0
2   1    1.38577    0
2   1   1.234877    0
2   1   1.071646    0
2   1   0.897708    0
2   1      0.7148   0
2   1    0.52475    0
2   1   0.329456    0
2   1   0.130871    0
2   1   -0.06902    0
2   1   -0.26822    0
2   1   -0.46475    0
2   1   -0.65663    0
2   1   -0.84195    0
2   1   -1.01885    0
2   1   -1.18558    0
2   1   -1.34046    0
2   1   -1.48195    0
2   1   -1.60862    0
2   1   -1.71923    0
2   1   -1.81266    0
2   1   -1.88798    0
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2   1   -1.98146    0
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2   1   -1.93085    0
2   1   -1.86916    0
2   1   -1.78879    0
2   1   -1.69055    0
2   1   -1.57541    0
2   1   -1.44453    0
2   1   -1.29923    0
2   1   -1.14094    0
2   1   -0.97124    0
2   1   -0.79185    0
2   1   -0.60454    0
2   1     -0.4112   0
2   1   -0.21374    0
2   1   -0.01415    0
2   1   0.185582    0
2   1   0.383461    0
2   1   0.577508    0
2   1   0.765784    0
2   1   0.946409    0
2   1   1.117578    0
2   1   1.277581    0
2   1   1.424818    0
2   1   1.557819    0
2   1   1.675255    0
2   1   1.775952    0
2   1   1.858904    0
2   1   1.923283    0
2   1   1.968445    0
2   1   1.993939    0
2   1    1.99951    0
2   1   1.985103    0
2   1   1.950861    0
2   1   1.897127    0
2   1   1.824438    0
2   1   1.733519    0
2   1    1.62528    0
2   1   1.500801    0
2   1   1.361327    0
2   1   1.208251    0
2   1   1.043102    0
2   1   0.867531    0
2   1   0.683292    0
2   1   0.492226    0
2   1   0.296241    0
2   1   0.097297    0
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2   1   -1.92181    0
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2   1   -1.77349    0
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1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
Second derivative
                                                             ACC
            -ab^2cos(bt+c)                                   /ACC/
                      -2     0      -0.4     0           2      2
             -1.9900083      0   -0.398      0         1.6    1.99
             -1.9601332      0   -0.392      0         1.2    1.96
               -1.910673     0   -0.382      0         0.8    1.911
               -1.842122     0   -0.368      0         0.4    1.842
             -1.7551651      0   -0.351      0           0    1.755
             -1.6506712      0     -0.33   1.6    -0.0584     1.651
             -1.5296844      0   -0.306    1.6   -0.04672     1.53
             -1.3934134      0   -0.279    1.6   -0.03504     1.393
             -1.2432199      0   -0.249    1.6   -0.02336     1.243
             -1.0806046      0   -0.216    1.6   -0.01168     1.081
             -0.9071922      0   -0.181    1.6           0    0.907
             -0.7247155      0   -0.145    3.2   -1.99659     0.725
             -0.5349977      0   -0.107    3.2   -1.59727     0.535
             -0.3399343      0   -0.068    3.2   -1.19795     0.34
             -0.1414744      0   -0.028    3.2   -0.79864     0.141
             0.05839904      0   0.0117    3.2   -0.39932     0.058
             0.25768899      0   0.0515
             0.45440419      0   0.0909    3.2          0 0.454
             0.45440419      0   0.0909                   0.454
             0.64657913      0   0.1293                   0.647
             1.00969221      0   0.2019                   1.01
             1.17700223      0   0.2354                   1.177
             1.33255204      0   0.2665                   1.333
             1.47478743      0    0.295                   1.475
             1.60228723      0   0.3205
             1.71377751      0   0.3428
             1.80814428      0   0.3616
1.88444468    0   0.3769
1.94191633    0   0.3884
1.97998499    0    0.396
 1.9982703    0   0.3997
1.99658955    0   0.3993
1.97495954    0    0.395
1.93359639    0   0.3867
1.87291337    0   0.3746
1.79351683    0   0.3587
1.69620006    0   0.3392
1.58193542    0   0.3164
1.45186461    0   0.2904
1.30728724    0   0.2615
1.14964789    0   0.2299
0.98052164    0   0.1961
0.80159834    0   0.1603
0.61466574    0   0.1229
 0.4215916    0   0.0843
0.22430505    0   0.0449
0.02477733    0    0.005
  -0.174998   0   -0.035
-0.3730247    0   -0.075
-0.5673244    0   -0.113
-0.7559555    0   -0.151
-0.9370333    0   -0.187
-1.1087487    0   -0.222
-1.2693858    0   -0.254
-1.4173395    0   -0.283
-1.5511318    0     -0.31
-1.6694256    0   -0.334
  -1.771039   0   -0.354
-1.8549569    0   -0.371
-1.9203406    0   -0.384
-1.9665369    0   -0.393
-1.9930842    0   -0.399
-1.9997173    0      -0.4
-1.9863698    0   -0.397
-1.9531753    0   -0.391
-1.9004652    0     -0.38
-1.8287663    0   -0.366
  -1.738795   0   -0.348
-1.6314502    0   -0.326
-1.5078045    0   -0.302
-1.3690933    0   -0.274
-1.2167026    0   -0.243
  -1.052155   0     -0.21
-0.8770947    0   -0.175
-0.6932706    0   -0.139
-0.5025197    0   -0.101
-0.3067477    0   -0.061
-0.1079108    0   -0.022
0.09200425    0   0.0184
0.29100007    0   0.0582
0.48708831    0   0.0974
0.67830972    0   0.1357
0.86275369    0   0.1726
1.03857731    0   0.2077
1.20402381    0   0.2408
1.35744009    0   0.2715
1.49729329    0   0.2995
1.62218603    0   0.3244
1.73087042    0   0.3462
1.82226052    0   0.3645
 1.8954432    0   0.3791
1.94968724    0   0.3899
1.98445065    0   0.3969
1.99938608    0   0.3999
1.99434431    0   0.3989
1.96937571    0   0.3939
1.92472976    0   0.3849
1.86085254    0   0.3722
1.77838231    0   0.3557
1.67814306    0   0.3356
1.56113636    0   0.3122
 1.4285313    0   0.2857
1.28165284    0   0.2563
1.12196851    0   0.2244
0.95107386    0   0.1902
0.77067638    0   0.1541
0.58257856    0   0.1165
0.38865981    0   0.0777
 0.1908577    0   0.0382
-0.0088514    0   -0.002
-0.2084721    0   -0.042
-0.4060097    0   -0.081
-0.5994907    0     -0.12
-0.7869817    0   -0.157
-0.9666095    0   -0.193
-1.1365793    0   -0.227
-1.2951927    0   -0.259
  -1.440865   0   -0.288
-1.5721406    0   -0.314
-1.6877079    0   -0.338
-1.7864122    0   -0.357
-1.8672673    0   -0.373
-1.9294652    0   -0.386
-1.9723846    0   -0.394
-1.9955966    0   -0.399
-1.9988692    0      -0.4
-1.9821697    0   -0.396
-1.9456651    0   -0.389
-1.8897201    0   -0.378
-1.8148936    0   -0.363
-1.7219332    0   -0.344
-1.6117679    0   -0.322
-1.4854983    0   -0.297
-1.3443862    0   -0.269
-1.1898413    0   -0.238
  -1.023408   0   -0.205
-0.8467491    0   -0.169
-0.6616298    0   -0.132
-0.4698996    0   -0.094
-0.2734744    0   -0.055
-0.0743168    0   -0.015
0.12558345    0   0.0251
0.32422887    0   0.0648
0.51963471    0   0.1039
0.70984853    0    0.142
0.89296978    0   0.1786
1.06716877    0   0.2134
1.23070497    0   0.2461
1.38194436    0   0.2764
1.51937583    0   0.3039
1.64162619    0   0.3283
1.74747397    0   0.3495
1.83586156    0   0.3672
1.90590583    0   0.3812
1.95690693    0   0.3914
1.98835525    0   0.3977
1.99993659    0       0.4
1.99153522    0   0.3983
1.96323509    0   0.3926
1.91531896    0   0.3831
 1.8482656    0   0.3697
1.76274498    0   0.3525
 1.6596116    0   0.3319
1.53989592    0    0.308
1.40479412    0    0.281
1.25565607    0   0.2511
1.09397193    0   0.2188
0.92135717    0   0.1843
0.73953653    0   0.1479
0.55032668    0   0.1101
0.35561814    0   0.0711
0.15735639    0   0.0315
-0.0424776    0   -0.008
-0.2418872    0   -0.048
-0.4388799    0   -0.088
-0.6314875    0   -0.126
-0.8177855    0   -0.164
-0.9959124    0   -0.199
-1.1640885    0   -0.233
-1.3206334    0   -0.264
  -1.463983   0   -0.293
-1.5927049    0   -0.319
-1.7055131    0   -0.341
-1.8012803    0     -0.36
-1.8790498    0   -0.376
-1.9380444    0   -0.388
-1.9776747    0   -0.396
-1.9975447    0      -0.4
-1.9974559    0   -0.399
-1.9774092    0   -0.395
-1.9376049    0   -0.388
-1.8784407    0   -0.376
-1.8005077    0     -0.36
-1.7045846    0   -0.341
-1.5916299    0   -0.318
-1.4627722    0   -0.293
-1.3192989    0   -0.264
-1.1626436    0   -0.233
-0.9943716    0   -0.199
-0.8161641    0   -0.163
-0.6298018    0   -0.126
-0.4371467    0   -0.087
-0.2401238    0   -0.048
-0.0407017    0   -0.008
0.15912713    0   0.0318
0.35736601    0   0.0715
 0.5520342    0   0.1104
0.74118665    0   0.1482
0.92293341    0   0.1846
1.09545852    0   0.2191
1.25703817    0   0.2514
1.40605791    0   0.2812
1.54102879    0   0.3082
1.66060222    0   0.3321
1.76358346    0   0.3527
1.84894355    0   0.3698
1.91582961    0   0.3832
1.96357334    0   0.3927
1.99169769    0   0.3983
1.99992165    0       0.4
1.98816306    0   0.3976
 1.9565394    0   0.3913
1.90536665    0   0.3811
 1.8351561    0    0.367
1.74660928    0   0.3493
1.64061092    0   0.3281
1.51822011    0   0.3036
1.38065975    0   0.2761
 1.2293043    0   0.2459
1.06566604    0   0.2131
    0.89138   0   0.1783
0.70818759    0   0.1416
 0.5179192    0   0.1036
0.32247593    0   0.0645
0.12381059    0   0.0248
-0.0760918    0   -0.015
  -0.275234   0   -0.055
  -0.471626   0   -0.094
-0.6633058    0   -0.133
  -0.848358   0     -0.17
-1.0249337    0   -0.205
-1.1912686    0   -0.238
-1.3457008    0   -0.269
-1.4866871    0   -0.297
  -1.612819   0   -0.323
-1.7228361    0   -0.345
-1.8156392    0   -0.363
  -1.890301   0   -0.378
-1.9460756    0   -0.389
-1.9824056    0   -0.396
-1.9989281    0      -0.4
  -1.995478   0   -0.399
-1.9720897    0   -0.394
-1.9289969    0   -0.386
-1.8666302    0   -0.373
-1.7856128    0   -0.357
-1.6867541    0   -0.337
  -1.571042   0   -0.314
-1.4396325    0   -0.288
-1.2938386    0   -0.259
-1.1351172    0   -0.227
-0.9650541    0   -0.193
-0.7853484    0   -0.157
-0.5977958    0     -0.12
-0.4042702    0   -0.081
-0.2067053    0   -0.041
-0.0070751    0   -0.001
0.19262583    0   0.0385
0.39040211    0   0.0781
0.58427762    0   0.1169
0.77231522    0   0.1545
 0.9526361    0   0.1905
1.12343855    0   0.2247
1.28301598    0   0.2566
1.42977394    0    0.286
1.56224607    0   0.3124
1.67910875    0   0.3358
1.77919433    0   0.3558
1.86150279    0   0.3723
1.92521173    0    0.385
1.96968459    0   0.3939
1.99447702    0   0.3989
1.99934129    0   0.3999
 1.9842288    0   0.3968
1.94929055    0   0.3899
1.89487564    0    0.379
1.82152775    0   0.3643
1.72997977    0    0.346
1.62114639    0   0.3242
1.49611506    0   0.2992
1.35613504    0   0.2712
1.20260497    0   0.2405
1.03705886    0   0.2074
0.86115081    0   0.1722
0.67663842    0   0.1353
0.48536529    0   0.0971
0.28924254    0   0.0578
0.09022978    0    0.018
-0.1096845    0   -0.022
-0.3085029    0   -0.062
-0.5042388    0   -0.101
-0.6949365    0   -0.139
-0.8786907    0   -0.176
-1.0536653    0   -0.211
  -1.218112   0   -0.244
-1.3703877    0   -0.274
-1.5089709    0   -0.302
  -1.632477   0   -0.326
  -1.739672   0   -0.348
-1.8294847    0   -0.366
-1.9010178    0     -0.38
-1.9535566    0   -0.391
-1.9865761    0   -0.397
-1.9997464    0      -0.4
-1.9929358    0   -0.399
-1.9662125    0   -0.393
-1.9198435    0   -0.384
  -1.854292   0   -0.371
-1.7702131    0   -0.354
-1.6684467    0   -0.334
-1.5500098    0     -0.31
-1.4160857    0   -0.283
-1.2680126    0   -0.254
-1.1072699    0   -0.221
-0.9354637    0   -0.187
-0.7543107    0   -0.151
-0.5656208    0   -0.113
-0.3712794    0   -0.074
-0.1732284    0   -0.035
0.02655349    0   0.0053
0.22607007    0   0.0452
0.42332783    0   0.0847
0.61635584    0   0.1233
0.80322543    0   0.1606
0.98206945    0   0.1964
1.15110096    0   0.2302
1.30863104    0   0.2617
1.45308572    0   0.2906
1.58302165    0   0.3166
1.69714055    0   0.3394
1.79430218    0   0.3589
1.87353574    0   0.3747
1.93404954    0   0.3868
1.97523897    0    0.395
1.99669245    0   0.3993
1.99819565    0   0.3996
1.97973354    0   0.3959
1.94149058    0   0.3883
1.88384889    0   0.3768
1.80738441    0   0.3615
1.71286114    0   0.3426
1.60122352    0   0.3202
1.47358701    0   0.2947
1.33122691    0   0.2662
1.17556563    0   0.2351
1.00815848    0   0.2016
0.83067815    0   0.1661
0.64489795    0    0.129
0.45267415    0   0.0905
0.25592738    0   0.0512
0.05662347    0   0.0113
-0.1432462    0   -0.029
-0.3416846    0   -0.068
  -0.536709   0   -0.107
-0.7263708    0   -0.145
-0.9087749    0   -0.182
-1.0820989    0   -0.216
-1.2446109    0   -0.249
-1.3946871    0   -0.279
-1.5308281    0   -0.306
-1.6516736    0     -0.33
  -1.756016   0   -0.351
  -1.842813   0   -0.369
-1.9111972    0   -0.382
-1.9604853    0   -0.392
-1.9901849    0   -0.398
-1.9999992    0      -0.4
-1.9898302    0   -0.398
-1.9597795    0   -0.392
-1.9101473    0   -0.382
-1.8414295    0   -0.368
-1.7543128    0   -0.351
-1.6496676    0     -0.33
-1.5285394    0   -0.306
-1.3921386    0   -0.278
  -1.241828   0   -0.248
-1.0791095    0   -0.216
-0.9056088    0   -0.181
-0.7230596    0   -0.145
-0.5332859    0   -0.107
-0.3381837    0   -0.068
-0.1397025    0   -0.028
0.06017458    0    0.012
0.25945039    0   0.0519
0.45613387    0   0.0912
 0.6482598    0   0.1297
0.83390854    0   0.1668
1.01122514    0   0.2022
1.17843791    0   0.2357
1.33387612    0   0.2668
1.47598668    0   0.2952
1.60334967    0   0.3207
1.71469252    0   0.3429
1.80890273    0   0.3618
1.88503898    0    0.377
1.94234055    0   0.3885
1.98023489    0    0.396
1.99834337
1.99648507
1.97467856
 1.9331417
1.87228953
1.79273007
1.69525824
1.58084795
1.45064235
1.30594241
1.14819392
0.97897306
0.79997063
0.61297515
0.41985503
0.22253986
0.02300114
-0.1767674
-0.3747697
-0.5690275
-0.7575997
-0.9386023
-1.1102266
-1.2707579
-1.4185923
-1.5522525
-1.6704031
-1.7718636
-1.8556203
-1.9208361
-1.9668597
  -1.993231
-1.9996866
  -1.986162
-1.9527924
  -1.899911
-1.8280464
-1.7379166
-1.6304221
-1.5066369
-1.3677979
-1.2152923
  -1.050644
-0.8754979
-0.6916042
-0.5008002
-0.3049923
-0.1061371
0.09377865
0.29275736
0.48881094
0.67998049
0.86435589
1.04009493
1.20544169
1.35874408
1.49847034
1.62322438
1.73175971
1.82299186
1.89600928
 1.9500824
1.98467094
 1.9994293
1.99421003
1.96906528
1.92424627
1.86020083
1.77756888
1.67717604
1.56002542
1.42728754
1.28028868
1.12049759
0.94951087
0.76903694
0.58087905
0.38691721
0.18908942
-0.0106277
-0.2102386
-0.4077489
-0.6011851
-0.7886144
-0.9681642
-1.1380404
-1.2965457
-1.4420963
  -1.573238
-1.6886604
-1.7872102
-1.8679029
-1.9299321
  -1.972678
-1.9957136
-1.9988087
-1.9819323
-1.9452531
-1.8891376
-1.8141465
  -1.721029
-1.6107156
-1.4843084
-1.3430705
-1.1884131
-1.0218814
-0.8451395
-0.6599532
-0.4681729
-0.2717147
-0.0725417
 0.1273562
0.32598156
0.52134982
0.71150892
0.89455886
1.06867066
1.23210466
1.38322788
1.52053034
1.64264017
1.74833727
1.83656557
1.90644352
 1.9572729
1.98854587
1.99994994
1.99137118
1.96289529
 1.9148068
1.84758619
1.76190512
1.65861967
1.53876184
1.40352921
1.25427298
1.09248447
0.91978021
0.73788582
0.54861872
0.35386999
0.15558552
-0.0442535
-0.2436504
-0.4406128
-0.6331727
-0.8194062
-0.9974524
-1.1655325
-1.3219669
-1.4651926
-1.5937787
-1.7064402
-1.8020516
-1.8796574
-1.9384823
-1.9779386
-1.9976319
-1.9973656
-1.9771422
-1.9371639
-1.8778301
-1.7997337
-1.7036548
-1.5905537
-1.4615602
-1.3179634
-1.1611978
   -0.99283
-0.8145421
-0.6281156
-0.4354132
-0.2383603
-0.0389257
0.16089775
 0.3591136
0.55374129
0.74283619
0.92450891
1.09694425
1.25841928
1.40732061
1.54216045
1.66159153
1.76442054
1.84962004
1.91633875
1.96391004
1.99185859
1.99990514
1.98796931
1.95617034
1.90482596
1.83444919
1.74574322
1.63959435
 1.5170632
1.37937405
1.22790266
1.06416247
0.88978952
0.70652608
0.51620327
0.32072273
0.12203763
-0.0778668
-0.2769933
-0.4733521
-0.6649813
-0.8499663
-1.0264587
  -1.192695
-1.3470143
-1.4878747
-1.6138688
-1.7237376
-1.8163834
-1.8908805
-1.9464845
-1.9826399
-1.9989855
-1.9953578
-1.9717932
  -1.928527
-1.8659917
  -1.784812
  -1.685799
-1.5699421
-1.4383988
-1.2924836
-1.1336543
-0.9634978
-0.7837145
-0.5961005
-0.4025304
-0.2049385
-0.0052988
0.19439381
 0.3921441
0.58597621
0.77395344
0.95419759
 1.1249077
1.28437811
1.43101544
1.56335454
1.68007311
1.78000495
1.86215157
1.92569219
1.96999192
1.99460815
1.99929491
1.98400538
1.94889232
1.89430658
1.82079355
1.72908775
1.62010548
1.49493565
1.35482891
1.20118518
 1.0355396
0.85954725
0.67496659
0.48364188
0.28748479
0.08845524
-0.1114581
-0.3102578
-0.5059575
-0.6966019
  -0.880286
-1.0551747
-1.2195203
-1.3716809
-1.5101362
-1.6335026
-1.7405476
-1.8302017
  -1.901569
-1.9539364
-1.9867808
-1.9997739
-1.9927859
-1.9658866
-1.9193449
-1.8536257
-1.7693857
-1.6674666
-1.5488867
-1.4148308
-1.2666384
-1.1057902
-0.9338933
-0.7526652
-0.5639168
-0.3695339
-0.1714587
0.02832964
0.22783491
0.42506373
0.61804546
0.80485187
0.98361648
1.15255311
1.30997382
1.45430569
1.58410663
 1.6980797
1.79508611
1.87415662
1.93450118
1.97551684
1.99679378
1.99811943
1.97948052
 1.9410633
1.88325162
1.80662311
1.71194342
1.60015856
1.47238544
1.32990073
1.17412809
1.00662396
0.82906197
0.64321626
0.45094376
0.25416557
0.05484784
-0.1450179
-0.3434347
   -0.53842
-0.7280256
-0.9103569
-1.0835923
-1.2460008
-1.3959597
-1.5319706
-1.6526746
-1.7568656
-1.8435025
-1.9117198
-1.9608359
-1.9903599
-1.9999968
-1.9896505
-1.9594243
-1.9096201
-1.8407356
-1.7534591
-1.6486627
-1.5273933
-1.3908627
-1.2404351
-1.0776135
-0.9040247
-0.7214032
-0.5315737
-0.3364328
-0.1379305
0.06195006
 0.2612116
0.45786319
0.64993996
0.83552275
1.01275728
1.17987266
1.33519915
1.47718477
1.60441085
1.71560619
1.80965975
 1.8856318
1.94276323
1.98048322
1.99841487
1.99637902
1.97439601
1.93268549
1.87166422
1.79194189
1.69431508
1.57975923
1.44941894
1.30459654
1.14673905
0.97742371
0.79834228
0.61128408
0.41811814
0.22077449
0.02122493
-0.1785367
-0.3765144
-0.5707302
-0.7592434
-0.9401704
-1.1117037
-1.2721291
-1.4198438
  -1.553372
-1.6713793
-1.7726868
-1.8562822
-1.9213302
-1.9671809
-1.9933762
-1.9996544
-1.9859526
-1.9524079
-1.8993554
-1.8273251
-1.7370368
-1.6293926
-1.5054681
-1.3665014
-1.2138811
-1.0491321
-0.8739005
-0.6899372
-0.4990802
-0.3032366
-0.1043632
0.09555297
0.29451443
0.49053319
0.68165072
0.86595741
1.04161174
1.20685863
1.36004699
1.49964621
1.62426146
1.73264763
1.82372175
1.89657385
1.95047601
1.98488966
1.99947095
1.99407418
1.96875329
1.92376126
1.85954765
1.77675405
1.67620771
1.55891326
1.42604266
1.27892351
1.11902579
0.94794713
0.76739689
0.57917908
 0.3851743
0.18732099
  -0.012404
  -0.212005
-0.4094877
  -0.602879
-0.7902465
-0.9697181
-1.1395007
-1.2978977
-1.4433265
-1.5743341
-1.6896115
-1.7880068
  -1.868537
-1.9303974
-1.9729698
  -1.995829
-1.9987466
-1.9816933
-1.9448396
-1.8885537
  -1.813398
-1.7201234
  -1.609662
-1.4831173
-1.3417538
-1.1869839
-1.0203541
-0.8435292
-0.6582761
-0.4664457
-0.2699547
-0.0707665
0.12912886
0.32773399
0.52306451
0.71316875
0.89614723
1.07017171
1.23350339
1.38451031
1.52168366
1.64365285
 1.7491992
1.83726814
1.90697969
1.95763734
1.98873492
1.99996172
1.99120557
1.96255394
1.91429313
1.84690533
1.76106386
1.65762643
1.53762654
1.40226319
 1.2528889
1.09099615
0.91820253
0.73623453
0.54691032
0.35212157
0.15381453
-0.0460294
-0.2454134
-0.4423453
-0.6348574
-0.8210263
-0.9989917
-1.1669755
-1.3232993
-1.4664011
-1.5948512
  -1.707366
-1.8028214
-1.8802635
-1.9389187
-1.9782009
-1.9977175
-1.9972737
-1.9768737
-1.9367214
-1.8772181
-1.7989582
-1.7027237
-1.5894762
-1.4603471
-1.3166268
-1.1597511
-0.9912876
-0.8129195
-0.6264289
-0.4336793
-0.2365965
-0.0371497
0.16266825
 0.3608609
0.55544795
0.74448514
0.92608369
1.09842912
 1.2597994
1.40858219
1.54329088
1.66257953
1.76525623
1.85029507
1.91684638
1.96424519
1.99201791
1.99988705
1.98777398
1.95579973
1.90428377
1.83374084
1.74487578
1.63857649
1.51590509
1.37808727
1.22650005
1.06265805
0.88819833
0.70486402
0.51448694
0.31896928
0.12026458
-0.0796418
-0.2787523
-0.4750777
-0.6666563
-0.8515739
-1.0279828
-1.1941204
-1.3483268
-1.4890612
-1.6149173
-1.7246377
-1.8171262
-1.8914585
-1.9468919
-1.9828727
-1.9990413
  -1.995236
-1.9714951
-1.9280556
-1.8653517
-1.7840097
-1.6848426
  -1.568841
-1.4371641
-1.2911275
-1.1321904
-0.9619409
-0.7820799
-0.5944047
-0.4007903
-0.2031714
-0.0035225
0.19616164
0.39388578
0.58767434
0.77559106
0.95575832
1.12637597
1.28573923
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                Type in required coefficients            Now consider the acceleration graph:
                  a       b      c
                   1      1          0                                  x =a cos(bt + c)
                                Radians

                          Displacement - time graph                                                      Acceleration - time
     x




            6                                                                                4




                                                                                       Acc
            5
                                                                                             3
            4
            3                                                                                2
            2
                                                                                             1
            1
            0                                                                                0
-1         -1   0.57          2.14                3.71   5.28    6.85             -1              0.57     2.14            3.71
                                                                                             -1
           -2
           -3                                                                                -2
           -4                                                                                -3
           -5
           -6                                                                                -4
                                            Time t                                                                Time t

                                 Velocity - time                               Put a = 3, b = 1 and c = 0
            4                                                                  What is velocity when acceleration is zero? Why?
     Vel




            3
                                                                               What is acceleration when velocity is zero? Why?
            2
            1                                                                  What is a when x = 0? x is max? min?
            0
                                                                               What is the relationship between x and a?
-1         -1   0.57          2.14                3.71   5.28    6.85

           -2                                                                  Put b = 2 and a = 1. Do your answers to the above still apply?
           -3
                                                                               What is the relationship between x and a?
           -4
                                                                               Explain.
                                         Time t
Starting value
    0
Increment
   0.1 Try 0.157
47.1   47.1       -1
47.2   47.2   -0.997
47.3   47.3   -0.985
47.4   47.4   -0.962
47.5   47.5    -0.93
47.6   47.6   -0.889
47.7   47.7   -0.839
47.8   47.8    -0.78
47.9   47.9   -0.714
48     48      -0.64
48.1   48.1    -0.56
48.2   48.2   -0.475
48.3   48.3   -0.385
48.4   48.4    -0.29
48.5   48.5   -0.193
48.6   48.6   -0.095
48.7   48.7    0.005
48.8   48.8    0.105
48.9   48.9    0.204
49     49      0.301
49.1   49.1    0.394
49.2   49.2    0.484
49.3   49.3    0.569
49.4   49.4    0.648
49.5   49.5    0.721
49.6   49.6    0.787
49.7   49.7    0.844
49.8   49.8    0.894
49.9   49.9    0.934
50     50      0.965
50.1   50.1    0.986
50.2   50.2    0.998
50.3   50.3    0.999
50.4   50.4    0.991
50.5   50.5    0.973
50.6   50.6    0.945
50.7   50.7    0.907
50.8   50.8    0.861
50.9   50.9    0.805
51     51      0.742
51.1   51.1    0.672
51.2   51.2    0.594
51.3   51.3    0.511
51.4   51.4    0.423
51.5   51.5     0.33
51.6   51.6    0.234
51.7   51.7    0.136
51.8   51.8    0.036
51.9   51.9   -0.064
52     52     -0.163
52.1   52.1   -0.261
52.2   52.2   -0.356
52.3   52.3   -0.447
52.4   52.4   -0.534
52.5   52.5   -0.616
52.6   52.6   -0.692
52.7   52.7    -0.76
52.8   52.8   -0.821
52.9   52.9   -0.874
53     53     -0.918
53.1   53.1   -0.953
53.2   53.2   -0.979
53.3   53.3   -0.994
53.4   53.4       -1
53.5   53.5   -0.996
53.6   53.6   -0.981
53.7   53.7   -0.957
53.8   53.8   -0.924
53.9   53.9   -0.881
54     54     -0.829
54.1   54.1   -0.769
54.2   54.2   -0.702
54.3   54.3   -0.627
54.4   54.4   -0.546
54.5   54.5    -0.46
54.6   54.6   -0.369
54.7   54.7   -0.274
54.8   54.8   -0.177
54.9   54.9   -0.078
55     55      0.022
55.1   55.1    0.122
55.2   55.2     0.22
55.3   55.3    0.317
55.4   55.4     0.41
55.5   55.5    0.499
55.6   55.6    0.583
55.7   55.7    0.661
55.8   55.8    0.733
55.9   55.9    0.797
56     56      0.853
56.1   56.1    0.901
56.2   56.2     0.94
56.3   56.3    0.969
56.4   56.4    0.989
56.5   56.5    0.999
56.6   56.6    0.999
56.7   56.7    0.989
56.8   56.8    0.969
56.9   56.9    0.939
57     57         0.9
57.1   57.1    0.852
57.2   57.2    0.795
57.3   57.3    0.731
57.4   57.4    0.659
57.5   57.5    0.581
57.6   57.6    0.496
57.7   57.7    0.407
57.8   57.8    0.314
57.9   57.9    0.218
58     58      0.119
58.1   58.1    0.019
58.2   58.2    -0.08
58.3   58.3    -0.18
58.4   58.4   -0.277
58.5   58.5   -0.371
58.6   58.6   -0.462
58.7   58.7   -0.548
58.8   58.8   -0.629
58.9   58.9   -0.704
59     59     -0.771
59.1   59.1   -0.831
59.2   59.2   -0.882
59.3   59.3   -0.925
59.4   59.4   -0.958
59.5   59.5   -0.982
59.6   59.6   -0.996
59.7   59.7       -1
59.8   59.8   -0.994
59.9   59.9   -0.978
60     60     -0.952
60.1   60.1   -0.917
60.2   60.2   -0.873
60.3   60.3    -0.82
60.4   60.4   -0.759
60.5   60.5    -0.69
60.6   60.6   -0.614
60.7   60.7   -0.532
60.8   60.8   -0.445
60.9   60.9   -0.353
61     61     -0.258
61.1   61.1    -0.16
61.2   61.2   -0.061
61.3   61.3    0.039
61.4   61.4    0.138
61.5   61.5    0.237
61.6   61.6    0.332
61.7   61.7    0.425
61.8   61.8    0.513
61.9   61.9    0.596
62     62      0.674
62.1   62.1    0.744
62.2   62.2    0.807
62.3   62.3    0.862
62.4   62.4    0.908
62.5   62.5    0.945
62.6   62.6    0.973
62.7   62.7    0.991
62.8   62.8    0.999
62.9   62.9    0.998
63     63      0.986
63.1   63.1    0.964
63.2   63.2    0.933
63.3   63.3    0.892
63.4   63.4    0.843
63.5   63.5    0.785
63.6   63.6    0.719
63.7   63.7    0.646
63.8   63.8    0.567
63.9   63.9    0.482
64     64      0.392
64.1   64.1    0.298
64.2   64.2    0.201
64.3   64.3    0.102
64.4   64.4    0.003
64.5   64.5   -0.097
64.6   64.6   -0.196
64.7   64.7   -0.293
64.8   64.8   -0.387
64.9   64.9   -0.477
65     65     -0.562
65.1   65.1   -0.642
65.2   65.2   -0.716
65.3   65.3   -0.782
65.4   65.4    -0.84
65.5   65.5    -0.89
65.6   65.6   -0.931
65.7   65.7   -0.963
65.8   65.8   -0.985
65.9   65.9   -0.997
66     66         -1
66.1   66.1   -0.992
66.2   66.2   -0.974
66.3   66.3   -0.947
66.4   66.4    -0.91
66.5   66.5   -0.865
66.6   66.6    -0.81
66.7   66.7   -0.747
66.8   66.8   -0.677
66.9   66.9   -0.601
67     67     -0.518
67.1   67.1    -0.43
67.2   67.2   -0.337
67.3   67.3   -0.242
67.4   67.4   -0.144
67.5   67.5   -0.044
67.6   67.6    0.056
67.7   67.7    0.155
67.8   67.8    0.253
67.9   67.9    0.348
68     68       0.44
68.1   68.1    0.528
68.2   68.2     0.61
68.3   68.3    0.686
68.4   68.4    0.755
68.5   68.5    0.817
68.6   68.6     0.87
68.7   68.7    0.915
68.8   68.8    0.951
68.9   68.9    0.977
69     69      0.993
69.1   69.1        1
69.2   69.2    0.996
69.3   69.3    0.983
69.4   69.4     0.96
69.5   69.5    0.927
69.6   69.6    0.885
69.7   69.7    0.834
69.8   69.8    0.774
69.9   69.9    0.707
70     70      0.633
70.1   70.1    0.553
70.2   70.2    0.467
70.3   70.3    0.376
70.4   70.4    0.282
70.5   70.5    0.185
70.6   70.6    0.086
70.7   70.7   -0.014
70.8   70.8   -0.114
70.9   70.9   -0.213
71     71     -0.309
71.1   71.1   -0.402
71.2   71.2   -0.492
71.3   71.3   -0.576
71.4   71.4   -0.655
71.5   71.5   -0.727
71.6   71.6   -0.792
71.7   71.7   -0.849
71.8   71.8   -0.898
71.9   71.9   -0.937
72     72     -0.967
72.1   72.1   -0.988
72.2   72.2   -0.998
72.3   72.3   -0.999
72.4   72.4    -0.99
72.5   72.5   -0.971
72.6   72.6   -0.942
72.7   72.7   -0.903
72.8   72.8   -0.856
72.9   72.9      -0.8
73     73     -0.736
73.1   73.1   -0.665
73.2   73.2   -0.587
73.3   73.3   -0.503
73.4   73.4   -0.415
73.5   73.5   -0.322
73.6   73.6   -0.225
73.7   73.7   -0.127
73.8   73.8   -0.027
73.9   73.9    0.073
74     74      0.172
74.1   74.1    0.269
74.2   74.2    0.364
74.3   74.3    0.455
74.4   74.4    0.542
74.5   74.5    0.623
74.6   74.6    0.698
74.7   74.7    0.766
74.8   74.8    0.826
74.9   74.9    0.878
75     75      0.922
75.1   75.1    0.956
75.2   75.2     0.98
75.3   75.3    0.995
75.4   75.4         1
75.5   75.5    0.995
75.6   75.6     0.98
75.7   75.7    0.955
75.8   75.8     0.92
75.9   75.9    0.877
76     76      0.824
76.1   76.1    0.764
76.2   76.2    0.695
76.3   76.3     0.62
76.4   76.4    0.539
76.5   76.5    0.452
76.6   76.6    0.361
76.7   76.7    0.266
76.8   76.8    0.168
76.9   76.9    0.069
77     77     -0.031
77.1   77.1   -0.131
77.2   77.2   -0.229
77.3   77.3   -0.325
77.4   77.4   -0.418
77.5   77.5   -0.506
77.6   77.6    -0.59
77.7   77.7   -0.668
77.8   77.8   -0.739
77.9   77.9   -0.802
78     78     -0.858
78.1   78.1   -0.905
78.2   78.2   -0.943
78.3   78.3   -0.971
78.4   78.4    -0.99
78.5   78.5   -0.999
78.6   78.6   -0.998
78.7   78.7   -0.987
78.8   78.8   -0.966
78.9   78.9   -0.936
79     79     -0.896
79.1   79.1   -0.847
79.2   79.2    -0.79
79.3   79.3   -0.725
79.4   79.4   -0.652
79.5   79.5   -0.573
79.6   79.6   -0.489
79.7   79.7   -0.399
79.8   79.8   -0.306
79.9   79.9   -0.209
80     80      -0.11
80.1   80.1   -0.011
80.2   80.2    0.089
80.3   80.3    0.188
80.4   80.4    0.285
80.5   80.5     0.38
80.6   80.6     0.47
80.7   80.7    0.556
80.8   80.8    0.636
80.9   80.9     0.71
81     81      0.777
81.1   81.1    0.836
81.2   81.2    0.886
81.3   81.3    0.928
81.4   81.4    0.961
81.5   81.5    0.984
81.6   81.6    0.997
81.7   81.7        1
81.8   81.8    0.993
81.9   81.9    0.976
82     82       0.95
82.1   82.1    0.914
82.2   82.2    0.869
82.3   82.3    0.815
82.4   82.4    0.753
82.5   82.5    0.683
82.6   82.6    0.607
82.7   82.7    0.525
82.8   82.8    0.437
82.9   82.9    0.345
83     83       0.25
83.1   83.1    0.152
83.2   83.2    0.052
83.3   83.3   -0.048
83.4   83.4   -0.147
83.5   83.5   -0.245
83.6   83.6   -0.341
83.7   83.7   -0.433
83.8   83.8   -0.521
83.9   83.9   -0.603
84     84      -0.68
84.1   84.1    -0.75
84.2   84.2   -0.812
84.3   84.3   -0.866
84.4   84.4   -0.912
84.5   84.5   -0.948
84.6   84.6   -0.975
84.7   84.7   -0.992
84.8   84.8       -1
84.9   84.9   -0.997
85     85     -0.984
85.1   85.1   -0.962
85.2   85.2    -0.93
85.3   85.3   -0.888
85.4   85.4   -0.838
85.5   85.5   -0.779
85.6   85.6   -0.713
85.7   85.7   -0.639
85.8   85.8    -0.56
85.9   85.9   -0.474
86     86     -0.384
86.1   86.1    -0.29
86.2   86.2   -0.193
86.3   86.3   -0.094
86.4   86.4    0.006
86.5   86.5    0.106
86.6   86.6    0.205
86.7   86.7    0.301
86.8   86.8    0.395
86.9   86.9    0.485
87     87       0.57
87.1   87.1    0.649
87.2   87.2    0.722
87.3   87.3    0.787
87.4   87.4    0.845
87.5   87.5    0.894
87.6   87.6    0.934
87.7   87.7    0.965
87.8   87.8    0.986
87.9   87.9    0.998
88     88      0.999
88.1   88.1    0.991
88.2   88.2    0.972
88.3   88.3    0.944
88.4   88.4    0.907
88.5   88.5     0.86
88.6   88.6    0.805
88.7   88.7    0.742
88.8   88.8    0.671
88.9   88.9    0.593
89     89       0.51
89.1   89.1    0.422
89.2   89.2    0.329
89.3   89.3    0.233
89.4   89.4    0.135
89.5   89.5    0.035
89.6   89.6   -0.065
89.7   89.7   -0.164
89.8   89.8   -0.262
89.9   89.9   -0.357
90     90     -0.448
90.1   90.1   -0.535
90.2   90.2   -0.617
90.3   90.3   -0.692
90.4   90.4   -0.761
90.5   90.5   -0.822
90.6   90.6   -0.875
90.7   90.7   -0.919
90.8   90.8   -0.953
90.9   90.9   -0.979
91     91     -0.994
91.1   91.1       -1
91.2   91.2   -0.996
91.3   91.3   -0.981
91.4   91.4   -0.957
91.5   91.5   -0.923
91.6   91.6   -0.881
91.7   91.7   -0.829
91.8   91.8   -0.769
91.9   91.9   -0.701
92     92     -0.626
92.1   92.1   -0.545
92.2   92.2   -0.459
92.3   92.3   -0.368
92.4   92.4   -0.273
92.5   92.5   -0.176
92.6   92.6   -0.077
92.7   92.7    0.023
92.8   92.8    0.123
92.9   92.9    0.221
93     93      0.317
93.1   93.1    0.411
93.2   93.2    0.499
93.3   93.3    0.583
93.4   93.4    0.662
93.5   93.5    0.733
93.6   93.6    0.797
93.7   93.7    0.854
93.8   93.8    0.901
93.9   93.9     0.94
94     94      0.969
94.1   94.1    0.989
94.2   94.2    0.999
94.3   94.3    0.999
94.4   94.4    0.988
94.5   94.5    0.968
94.6   94.6    0.939
94.7   94.7    0.899
94.8   94.8    0.851
94.9   94.9    0.795
95     95       0.73
95.1   95.1    0.658
95.2   95.2     0.58
95.3   95.3    0.496
95.4   95.4    0.406
95.5   95.5    0.313
95.6   95.6    0.217
95.7   95.7    0.118
95.8   95.8    0.019
95.9   95.9   -0.081
96     96      -0.18
96.1   96.1   -0.278
96.2   96.2   -0.372
96.3   96.3   -0.463
96.4   96.4   -0.549
96.5   96.5    -0.63
96.6   96.6   -0.704
96.7   96.7   -0.772
96.8   96.8   -0.831
96.9   96.9   -0.883
97     97     -0.925
97.1   97.1   -0.958
97.2   97.2   -0.982
97.3    97.3    -0.996
97.4    97.4        -1
97.5    97.5    -0.994
97.6    97.6    -0.978
97.7    97.7    -0.952
97.8    97.8    -0.917
97.9    97.9    -0.872
 98      98     -0.819
98.1    98.1    -0.758
98.2    98.2    -0.689
98.3    98.3    -0.613
98.4    98.4    -0.531
98.5    98.5    -0.444
98.6    98.6    -0.352
98.7    98.7    -0.257
98.8    98.8    -0.159
98.9    98.9     -0.06
 99      99       0.04
99.1    99.1     0.139
99.2    99.2     0.238
99.3    99.3     0.333
99.4    99.4     0.426
99.5    99.5     0.514
99.6    99.6     0.597
99.7    99.7     0.674
99.8    99.8     0.745
99.9    99.9     0.807
100     100      0.862
100.1   100.1    0.909
100.2   100.2    0.946
100.3   100.3    0.973
100.4   100.4    0.991
100.5   100.5        1
100.6   100.6    0.998
100.7   100.7    0.986
100.8   100.8    0.964
100.9   100.9    0.933
101     101      0.892
101.1   101.1    0.842
101.2   101.2    0.784
101.3   101.3    0.719
101.4   101.4    0.646
101.5   101.5    0.566
101.6   101.6    0.481
101.7   101.7    0.391
101.8   101.8    0.297
101.9   101.9       0.2
102     102      0.102
102.1   102.1    0.002
102.2   102.2   -0.098
102.3   102.3   -0.197
102.4   102.4   -0.294
102.5   102.5   -0.388
102.6   102.6   -0.478
102.7   102.7   -0.563
102.8   102.8   -0.643
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                                    t    x      y             Velocity

                                         t     a cos(bt+c)     vectors     Speed
                                   0     0         1                     | velocity |                                                                     Second derivative
                                   0.1   0.1       1            1.00                  Derivative                        velocity vectors         speed
                                   0.2   0.2   0.98             0.00            1              1 -ab sin(bt+c)                                   \vel\              0
                                   0.3   0.3   0.96                                            1           0 0.2      0           0          1      1               0
                                   0.4   0.4   0.92              1.00                          1 -0.09983 0.2      -0.2         0.2          1    1.005             0
                                   0.5   0.5   0.88             -0.10        1.005             1 -0.19867 0.2 0.0117            0.4          1    1.02              0
                                   0.6   0.6   0.83                                            1 -0.29552 0.2 -0.059            0.6          1    1.043             0
                                   0.7   0.7   0.76              1.00                          1 -0.38942 0.2 -0.078            0.8          1    1.073             0
                                   0.8   0.8     0.7            -0.20         1.02             1 -0.47943 0.2 -0.096              1          1    1.109             0
                5.28        6.85   0.9   0.9   0.62                                            1 -0.56464 0.2 -0.113            1.6    -0.0292    1.148             0
                                   1     1     0.54                                            1 -0.64422 0.2 -0.129            1.8 -0.22911      1.19              0
                                   1.1   1.1   0.45          Acceleration| acceleration |      1 -0.71736 0.2 -0.143              2 -0.42903      1.231             0
                                   1.2   1.2   0.36            vectors                         1 -0.78333 0.2 -0.157            2.2 -0.62894      1.27              0
                                   1.3   1.3   0.27                                            1 -0.84147 0.2 -0.168            2.4 -0.82886      1.307             0
                                   1.4   1.4   0.17              0.00                          1 -0.89121 0.2 -0.178            2.6 -1.02877      1.339             0
                                   1.5   1.5   0.07             -1.00           1              1 -0.93204 0.2 -0.186            3.2 -0.99829      1.367             0
                                   1.6   1.6      -0                                           1 -0.96356 0.2 -0.193            3.4 -0.98662      1.389             0
                                   1.7   1.7    -0.1             0.00                          1 -0.98545 0.2 -0.197            3.6 -0.97495      1.404             0
                                   1.8   1.8    -0.2            -1.00        0.995             1 -0.99749 0.2 -0.199            3.8 -0.96327      1.412             0
                                   1.9   1.9    -0.3                                           1 -0.99957 0.2      -0.2           4    -0.9516    1.414             0
                                   2     2      -0.4                                           1 -0.99166 0.2 -0.198            4.2 -0.93992      1.408             0
                                   2.1   2.1    -0.5             0.00                          1 -0.97385 0.2 -0.195            4.2 -0.93992      1.396             0
                                   2.2   2.2    -0.6            -0.98         0.98             1    -0.9463 0.2 -0.189                            1.377             0
                                   2.3   2.3    -0.7                                           1    -0.9093 0.2 -0.182                            1.352             0
                                   2.4   2.4    -0.7                                           1 -0.86321 0.2 -0.173                              1.321             0
to the above still apply?          2.5   2.5    -0.8                                           1    -0.8085 0.2 -0.162                            1.286             0
                                   2.6   2.6    -0.9                                           1 -0.74571 0.2 -0.149                              1.247             0
                                   2.7   2.7    -0.9                                           1 -0.67546 0.2 -0.135                              1.207             0
                                   2.8   2.8    -0.9                                           1 -0.59847 0.2    -0.12                                              0
                                   2.9   2.9      -1                                           1    -0.5155 0.2 -0.103                                              0
                                   3     3        -1                                           1 -0.42738 0.2 -0.085                                                0
3.1   3.1     -1   1   -0.33499   0.2   -0.067    0
3.2   3.2     -1   1   -0.23925   0.2   -0.048    0
3.3   3.3     -1   1   -0.14112   0.2   -0.028    0
3.4   3.4     -1   1   -0.04158   0.2   -0.008    0
3.5   3.5   -0.9   1   0.058374   0.2   0.0117    0
3.6   3.6   -0.9   1   0.157746   0.2   0.0315    0
3.7   3.7   -0.8   1   0.255541   0.2   0.0511    0
3.8   3.8   -0.8   1   0.350783   0.2   0.0702    0
3.9   3.9   -0.7   1    0.44252   0.2   0.0885    0
4     4     -0.7   1   0.529836   0.2    0.106    0
4.1   4.1   -0.6   1   0.611858   0.2   0.1224    0
4.2   4.2   -0.5   1   0.687766   0.2   0.1376    0
4.3   4.3   -0.4   1   0.756802   0.2   0.1514    0
4.4   4.4   -0.3   1   0.818277   0.2   0.1637    0
4.5   4.5   -0.2   1   0.871576   0.2   0.1743    0
4.6   4.6   -0.1   1   0.916166   0.2   0.1832    0
4.7   4.7     -0   1   0.951602   0.2   0.1903    0
4.8   4.8   0.09   1    0.97753   0.2   0.1955    0
4.9   4.9   0.19   1   0.993691   0.2   0.1987    0
5     5     0.28   1   0.999923   0.2       0.2   0
5.1   5.1   0.38   1   0.996165   0.2   0.1992    0
5.2   5.2   0.47   1   0.982453   0.2   0.1965    0
5.3   5.3   0.55   1   0.958924   0.2   0.1918    0
5.4   5.4   0.63   1   0.925815   0.2   0.1852    0
5.5   5.5   0.71   1   0.883455   0.2   0.1767    0
5.6   5.6   0.78   1   0.832267   0.2   0.1665    0
5.7   5.7   0.83   1   0.772764   0.2   0.1546    0
5.8   5.8   0.89   1    0.70554   0.2   0.1411    0
5.9   5.9   0.93   1   0.631267   0.2   0.1263    0
6     6     0.96   1   0.550686   0.2   0.1101    0
6.1   6.1   0.98   1   0.464602   0.2   0.0929    0
6.2   6.2      1   1   0.373877   0.2   0.0748    0
6.3   6.3      1   1   0.279415   0.2   0.0559    0
6.4   6.4   0.99   1   0.182163   0.2   0.0364    0
6.5   6.5   0.98   1   0.083089   0.2   0.0166    0
6.6   6.6   0.95   1 -0.01681 0.2 -0.003     0
6.7   6.7   0.91   1 -0.11655 0.2 -0.023     0
6.8   6.8   0.87   1 -0.21512 0.2 -0.043     0
6.9   6.9   0.82   1 -0.31154 0.2 -0.062     0
7     7     0.75   1 -0.40485 0.2 -0.081     0
7.1   7.1   0.68   1 -0.49411 0.2 -0.099     0
7.2   7.2   0.61   1 -0.57844 0.2 -0.116     0
7.3   7.3   0.53   1 -0.65699 0.2 -0.131     0
7.4   7.4   0.44   1 -0.72897 0.2 -0.146     0
7.5   7.5   0.35   1 -0.79367 0.2 -0.159     0
7.6   7.6   0.25   1 -0.85044 0.2   -0.17    0
7.7   7.7   0.15   1 -0.89871 0.2   -0.18    0
7.8   7.8   0.05   1    -0.938 0.2 -0.188    0
7.9   7.9     -0   1 -0.96792 0.2 -0.194     0
8     8     -0.1   1 -0.98817 0.2 -0.198     0
8.1   8.1   -0.2   1 -0.99854 0.2     -0.2   0
8.2   8.2   -0.3   1 -0.99894 0.2     -0.2   0
8.3   8.3   -0.4   1 -0.98936 0.2 -0.198     0
8.4   8.4   -0.5   1 -0.96989 0.2 -0.194     0
8.5   8.5   -0.6   1 -0.94073 0.2 -0.188     0
8.6   8.6   -0.7   1 -0.90217 0.2   -0.18    0
8.7   8.7   -0.7   1   -0.8546 0.2 -0.171    0
8.8   8.8   -0.8   1 -0.79849 0.2   -0.16    0
8.9   8.9   -0.9   1   -0.7344 0.2 -0.147    0
9     9     -0.9   1 -0.66297 0.2 -0.133     0
9.1   9.1   -0.9   1 -0.58492 0.2 -0.117     0
9.2   9.2     -1   1 -0.50102 0.2     -0.1   0
9.3   9.3     -1   1 -0.41212 0.2 -0.082     0
9.4   9.4     -1   1   -0.3191 0.2 -0.064    0
9.5   9.5     -1   1 -0.22289 0.2 -0.045     0
9.6   9.6     -1   1 -0.12445 0.2 -0.025     0
9.7   9.7     -1   1 -0.02478 0.2 -0.005     0
9.8   9.8   -0.9   1 0.075151 0.2 0.015      0
9.9   9.9   -0.9   1 0.174327 0.2 0.0349     0
10    10    -0.8   1 0.271761 0.2 0.0544     0
10.1   10.1   -0.8   1   0.366479   0.2   0.0733    0
10.2   10.2   -0.7   1   0.457536   0.2   0.0915    0
10.3   10.3   -0.6   1   0.544021   0.2   0.1088    0
10.4   10.4   -0.6   1   0.625071   0.2    0.125    0
10.5   10.5   -0.5   1   0.699875   0.2      0.14   0
10.6   10.6   -0.4   1   0.767686   0.2   0.1535    0
10.7   10.7   -0.3   1   0.827826   0.2   0.1656    0
10.8   10.8   -0.2   1   0.879696   0.2   0.1759    0
10.9   10.9   -0.1   1   0.922775   0.2   0.1846    0
11     11        0   1   0.956635   0.2   0.1913    0
11.1   11.1    0.1   1   0.980936   0.2   0.1962    0
11.2   11.2    0.2   1   0.995436   0.2   0.1991    0
11.3   11.3    0.3   1    0.99999   0.2       0.2   0
11.4   11.4   0.39   1   0.994553   0.2   0.1989    0
11.5   11.5   0.48   1   0.979178   0.2   0.1958    0
11.6   11.6   0.57   1   0.954019   0.2   0.1908    0
11.7   11.7   0.65   1   0.919329   0.2   0.1839    0
11.8   11.8   0.72   1   0.875452   0.2   0.1751    0
11.9   11.9   0.79   1   0.822829   0.2   0.1646    0
12     12     0.84   1   0.761984   0.2   0.1524    0
12.1   12.1   0.89   1   0.693525   0.2   0.1387    0
12.2   12.2   0.93   1   0.618137   0.2   0.1236    0
12.3   12.3   0.96   1   0.536573   0.2   0.1073    0
12.4   12.4   0.99   1   0.449647   0.2   0.0899    0
12.5   12.5      1   1   0.358229   0.2   0.0716    0
12.6   12.6      1   1   0.263232   0.2   0.0526    0
12.7   12.7   0.99   1   0.165604   0.2   0.0331    0
12.8   12.8   0.97   1   0.066322   0.2   0.0133    0
12.9   12.9   0.94   1   -0.03362   0.2   -0.007    0
13     13     0.91   1   -0.13323   0.2   -0.027    0
13.1   13.1   0.86   1   -0.23151   0.2   -0.046    0
13.2   13.2   0.81   1   -0.32747   0.2   -0.065    0
13.3   13.3   0.74   1   -0.42017   0.2   -0.084    0
13.4   13.4   0.67   1   -0.50866   0.2   -0.102    0
13.5   13.5   0.59   1   -0.59207   0.2   -0.118    0
13.6   13.6   0.51   1   -0.66957    0.2   -0.134    0
13.7   13.7   0.42   1   -0.74038    0.2   -0.148    0
13.8   13.8   0.33   1   -0.80378    0.2   -0.161    0
13.9   13.9   0.23   1   -0.85916    0.2   -0.172    0
14     14     0.14   1   -0.90595    0.2   -0.181    0
14.1   14.1   0.04   1     -0.9437   0.2   -0.189    0
14.2   14.2   -0.1   1   -0.97201    0.2   -0.194    0
14.3   14.3   -0.2   1   -0.99061    0.2   -0.198    0
14.4   14.4   -0.3   1   -0.99931    0.2      -0.2   0
14.5   14.5   -0.4   1   -0.99803    0.2      -0.2   0
14.6   14.6   -0.4   1   -0.98677    0.2   -0.197    0
14.7   14.7   -0.5   1   -0.96566    0.2   -0.193    0
14.8   14.8   -0.6   1     -0.9349   0.2   -0.187    0
14.9   14.9   -0.7   1   -0.89479    0.2   -0.179    0
15     15     -0.8   1   -0.84575    0.2   -0.169    0
15.1   15.1   -0.8   1   -0.78825    0.2   -0.158    0
15.2   15.2   -0.9   1   -0.72288    0.2   -0.145    0
15.3   15.3   -0.9   1   -0.65029    0.2     -0.13   0
15.4   15.4     -1   1     -0.5712   0.2   -0.114    0
15.5   15.5     -1   1     -0.4864   0.2   -0.097    0
15.6   15.6     -1   1   -0.39674    0.2   -0.079    0
15.7   15.7     -1   1   -0.30312    0.2   -0.061    0
15.8   15.8     -1   1   -0.20647    0.2   -0.041    0
15.9   15.9     -1   1   -0.10775    0.2   -0.022    0
16     16       -1   1   -0.00796    0.2   -0.002    0
16.1   16.1   -0.9   1   0.091907    0.2   0.0184    0
16.2   16.2   -0.9   1   0.190859    0.2   0.0382    0
16.3   16.3   -0.8   1   0.287903    0.2   0.0576    0
16.4   16.4   -0.8   1   0.382071    0.2   0.0764    0
16.5   16.5   -0.7   1   0.472422    0.2   0.0945    0
16.6   16.6   -0.6   1   0.558052    0.2   0.1116    0
16.7   16.7   -0.5   1   0.638107    0.2   0.1276    0
16.8   16.8   -0.5   1   0.711785    0.2   0.1424    0
16.9   16.9   -0.4   1   0.778352    0.2   0.1557    0
17     17     -0.3   1   0.837142    0.2   0.1674    0
17.1   17.1   -0.2   1   0.887567    0.2   0.1775    0
17.2   17.2   -0.1   1   0.929124    0.2   0.1858    0
17.3   17.3   0.02   1   0.961397    0.2   0.1923    0
17.4   17.4   0.12   1   0.984065    0.2   0.1968    0
17.5   17.5   0.22   1      0.9969   0.2   0.1994    0
17.6   17.6   0.32   1   0.999774    0.2       0.2   0
17.7   17.7   0.41   1   0.992659    0.2   0.1985    0
17.8   17.8    0.5   1   0.975626    0.2   0.1951    0
17.9   17.9   0.58   1   0.948844    0.2   0.1898    0
18     18     0.66   1   0.912582    0.2   0.1825    0
18.1   18.1   0.73   1   0.867202    0.2   0.1734    0
18.2   18.2    0.8   1   0.813157    0.2   0.1626    0
18.3   18.3   0.85   1   0.750987    0.2   0.1502    0
18.4   18.4    0.9   1   0.681314    0.2   0.1363    0
18.5   18.5   0.94   1   0.604833    0.2    0.121    0
18.6   18.6   0.97   1   0.522309    0.2   0.1045    0
18.7   18.7   0.99   1   0.434566    0.2   0.0869    0
18.8   18.8      1   1   0.342481    0.2   0.0685    0
18.9   18.9      1   1   0.246974    0.2   0.0494    0
19     19     0.99   1   0.148999    0.2   0.0298    0
19.1   19.1   0.97   1   0.049536    0.2   0.0099    0
19.2   19.2   0.94   1   -0.05042    0.2     -0.01   0
19.3   19.3    0.9   1   -0.14988    0.2     -0.03   0
19.4   19.4   0.85   1   -0.24783    0.2     -0.05   0
19.5   19.5    0.8   1   -0.34331    0.2   -0.069    0
19.6   19.6   0.73   1   -0.43537    0.2   -0.087    0
19.7   19.7   0.66   1   -0.52307    0.2   -0.105    0
19.8   19.8   0.58   1   -0.60554    0.2   -0.121    0
19.9   19.9    0.5   1   -0.68196    0.2   -0.136    0
20     20     0.41   1   -0.75157    0.2     -0.15   0
20.1   20.1   0.31   1   -0.81367    0.2   -0.163    0
20.2   20.2   0.22   1   -0.86764    0.2   -0.174    0
20.3   20.3   0.12   1   -0.91295    0.2   -0.183    0
20.4   20.4   0.02   1   -0.94912    0.2     -0.19   0
20.5   20.5   -0.1   1   -0.97582    0.2   -0.195    0
20.6   20.6   -0.2   1   -0.99277    0.2   -0.199    0
20.7   20.7   -0.3   1   -0.99979    0.2      -0.2   0
20.8   20.8   -0.4   1   -0.99683    0.2   -0.199    0
20.9   20.9   -0.5   1   -0.98391    0.2   -0.197    0
21     21     -0.5   1   -0.96115    0.2   -0.192    0
21.1   21.1   -0.6   1     -0.9288   0.2   -0.186    0
21.2   21.2   -0.7   1   -0.88716    0.2   -0.177    0
21.3   21.3   -0.8   1   -0.83666    0.2   -0.167    0
21.4   21.4   -0.8   1   -0.77779    0.2   -0.156    0
21.5   21.5   -0.9   1   -0.71116    0.2   -0.142    0
21.6   21.6   -0.9   1   -0.63742    0.2   -0.127    0
21.7   21.7     -1   1   -0.55732    0.2   -0.111    0
21.8   21.8     -1   1   -0.47164    0.2   -0.094    0
21.9   21.9     -1   1   -0.38125    0.2   -0.076    0
22     22       -1   1   -0.28705    0.2   -0.057    0
22.1   22.1     -1   1   -0.18999    0.2   -0.038    0
22.2   22.2     -1   1   -0.09102    0.2   -0.018    0
22.3   22.3     -1   1   0.008851    0.2   0.0018    0
22.4   22.4   -0.9   1   0.108637    0.2   0.0217    0
22.5   22.5   -0.9   1   0.207336    0.2   0.0415    0
22.6   22.6   -0.8   1   0.303965    0.2   0.0608    0
22.7   22.7   -0.8   1   0.397556    0.2   0.0795    0
22.8   22.8   -0.7   1   0.487175    0.2   0.0974    0
22.9   22.9   -0.6   1   0.571926    0.2   0.1144    0
23     23     -0.5   1   0.650962    0.2   0.1302    0
23.1   23.1   -0.4   1   0.723495    0.2   0.1447    0
23.2   23.2   -0.4   1   0.788798    0.2   0.1578    0
23.3   23.3   -0.3   1    0.84622    0.2   0.1692    0
23.4   23.4   -0.2   1   0.895187    0.2    0.179    0
23.5   23.5   -0.1   1    0.93521    0.2    0.187    0
23.6   23.6   0.04   1   0.965888    0.2   0.1932    0
23.7   23.7   0.14   1   0.986916    0.2   0.1974    0
23.8   23.8   0.24   1   0.998082    0.2   0.1996    0
23.9   23.9   0.33   1   0.999276    0.2   0.1999    0
24     24     0.42   1   0.990486    0.2   0.1981    0
24.1   24.1   0.51   1   0.971798   0.2   0.1944    0
24.2   24.2    0.6   1   0.943401   0.2   0.1887    0
24.3   24.3   0.67   1   0.905578   0.2   0.1811    0
24.4   24.4   0.74   1   0.858707   0.2   0.1717    0
24.5   24.5   0.81   1   0.803256   0.2   0.1607    0
24.6   24.6   0.86   1   0.739779   0.2    0.148    0
24.7   24.7   0.91   1    0.66891   0.2   0.1338    0
24.8   24.8   0.95   1   0.591358   0.2   0.1183    0
24.9   24.9   0.97   1   0.507897   0.2   0.1016    0
25     25     0.99   1   0.419361   0.2   0.0839    0
25.1   25.1      1   1   0.326635   0.2   0.0653    0
25.2   25.2      1   1   0.230646   0.2   0.0461    0
25.3   25.3   0.99   1   0.132352   0.2   0.0265    0
25.4   25.4   0.96   1   0.032735   0.2   0.0065    0
25.5   25.5   0.93   1   -0.06721   0.2   -0.013    0
25.6   25.6   0.89   1   -0.16648   0.2   -0.033    0
25.7   25.7   0.84   1   -0.26409   0.2   -0.053    0
25.8   25.8   0.79   1   -0.35906   0.2   -0.072    0
25.9   25.9   0.72   1   -0.45044   0.2     -0.09   0
26     26     0.65   1   -0.53732   0.2   -0.107    0
26.1   26.1   0.57   1   -0.61884   0.2   -0.124    0
26.2   26.2   0.48   1   -0.69416   0.2   -0.139    0
26.3   26.3   0.39   1   -0.76256   0.2   -0.153    0
26.4   26.4    0.3   1   -0.82333   0.2   -0.165    0
26.5   26.5    0.2   1   -0.87588   0.2   -0.175    0
26.6   26.6    0.1   1   -0.91968   0.2   -0.184    0
26.7   26.7      0   1   -0.95429   0.2   -0.191    0
26.8   26.8   -0.1   1   -0.97936   0.2   -0.196    0
26.9   26.9   -0.2   1   -0.99464   0.2   -0.199    0
27     27     -0.3   1   -0.99999   0.2      -0.2   0
27.1   27.1   -0.4   1   -0.99535   0.2   -0.199    0
27.2   27.2   -0.5   1   -0.98076   0.2   -0.196    0
27.3   27.3   -0.6   1   -0.95638   0.2   -0.191    0
27.4   27.4   -0.6   1   -0.92243   0.2   -0.184    0
27.5   27.5   -0.7   1   -0.87927   0.2   -0.176    0
27.6   27.6   -0.8   1   -0.82733    0.2   -0.165    0
27.7   27.7   -0.8   1   -0.76712    0.2   -0.153    0
27.8   27.8   -0.9   1   -0.69924    0.2     -0.14   0
27.9   27.9   -0.9   1   -0.62438    0.2   -0.125    0
28     28       -1   1   -0.54328    0.2   -0.109    0
28.1   28.1     -1   1   -0.45675    0.2   -0.091    0
28.2   28.2     -1   1   -0.36565    0.2   -0.073    0
28.3   28.3     -1   1   -0.27091    0.2   -0.054    0
28.4   28.4     -1   1   -0.17345    0.2   -0.035    0
28.5   28.5     -1   1   -0.07427    0.2   -0.015    0
28.6   28.6   -0.9   1   0.025663    0.2   0.0051    0
28.7   28.7   -0.9   1   0.125336    0.2   0.0251    0
28.8   28.8   -0.9   1   0.223756    0.2   0.0448    0
28.9   28.9   -0.8   1    0.31994    0.2    0.064    0
29     29     -0.7   1   0.412928    0.2   0.0826    0
29.1   29.1   -0.7   1   0.501789    0.2   0.1004    0
29.2   29.2   -0.6   1   0.585637    0.2   0.1171    0
29.3   29.3   -0.5   1   0.663634    0.2   0.1327    0
29.4   29.4   -0.4   1       0.735   0.2    0.147    0
29.5   29.5   -0.3   1   0.799021    0.2   0.1598    0
29.6   29.6   -0.2   1    0.85506    0.2    0.171    0
29.7   29.7   -0.1   1   0.902555    0.2   0.1805    0
29.8   29.8     -0   1   0.941031    0.2   0.1882    0
29.9   29.9   0.05   1   0.970106    0.2    0.194    0
30     30     0.15   1   0.989487    0.2   0.1979    0
30.1   30.1   0.25   1   0.998982    0.2   0.1998    0
30.2   30.2   0.35   1   0.998495    0.2   0.1997    0
30.3   30.3   0.44   1   0.988032    0.2   0.1976    0
30.4   30.4   0.53   1   0.967696    0.2   0.1935    0
30.5   30.5   0.61   1   0.937692    0.2   0.1875    0
30.6   30.6   0.69   1   0.898318    0.2   0.1797    0
30.7   30.7   0.75   1   0.849969    0.2      0.17   0
30.8   30.8   0.82   1   0.793127    0.2   0.1586    0
30.9   30.9   0.87   1   0.728361    0.2   0.1457    0
31     31     0.91   1   0.656317    0.2   0.1313    0
31.1   31.1   0.95   1   0.577715    0.2   0.1155    0
31.2   31.2   0.98   1   0.493341    0.2   0.0987    0
31.3   31.3   0.99   1   0.404038    0.2   0.0808    0
31.4   31.4      1   1   0.310697    0.2   0.0621    0
31.5   31.5      1   1   0.214253    0.2   0.0429    0
31.6   31.6   0.98   1   0.115667    0.2   0.0231    0
31.7   31.7   0.96   1   0.015926    0.2   0.0032    0
31.8   31.8   0.93   1   -0.08397    0.2   -0.017    0
31.9   31.9   0.89   1   -0.18304    0.2   -0.037    0
32     32     0.83   1   -0.28027    0.2   -0.056    0
32.1   32.1   0.78   1     -0.3747   0.2   -0.075    0
32.2   32.2   0.71   1   -0.46539    0.2   -0.093    0
32.3   32.3   0.63   1   -0.55143    0.2     -0.11   0
32.4   32.4   0.55   1   -0.63196    0.2   -0.126    0
32.5   32.5   0.47   1   -0.70617    0.2   -0.141    0
32.6   32.6   0.38   1   -0.77333    0.2   -0.155    0
32.7   32.7   0.28   1   -0.83276    0.2   -0.167    0
32.8   32.8   0.19   1   -0.88387    0.2   -0.177    0
32.9   32.9   0.09   1   -0.92615    0.2   -0.185    0
33     33       -0   1   -0.95918    0.2   -0.192    0
33.1   33.1   -0.1   1   -0.98262    0.2   -0.197    0
33.2   33.2   -0.2   1   -0.99624    0.2   -0.199    0
33.3   33.3   -0.3   1   -0.99991    0.2      -0.2   0
33.4   33.4   -0.4   1   -0.99359    0.2   -0.199    0
33.5   33.5   -0.5   1   -0.97734    0.2   -0.195    0
33.6   33.6   -0.6   1   -0.95133    0.2     -0.19   0
33.7   33.7   -0.7   1   -0.91581    0.2   -0.183    0
33.8   33.8   -0.7   1   -0.87114    0.2   -0.174    0
33.9   33.9   -0.8   1   -0.81777    0.2   -0.164    0
34     34     -0.8   1   -0.75622    0.2   -0.151    0
34.1   34.1   -0.9   1   -0.68712    0.2   -0.137    0
34.2   34.2   -0.9   1   -0.61116    0.2   -0.122    0
34.3   34.3     -1   1   -0.52908    0.2   -0.106    0
34.4   34.4     -1   1   -0.44172    0.2   -0.088    0
34.5   34.5     -1   1   -0.34995    0.2     -0.07   0
34.6   34.6     -1   1   -0.25468    0.2    -0.051   0
34.7   34.7     -1   1   -0.15687    0.2    -0.031   0
34.8   34.8     -1   1   -0.05749    0.2    -0.011   0
34.9   34.9   -0.9   1   0.042468    0.2   0.0085    0
35     35     -0.9   1   0.141999    0.2   0.0284    0
35.1   35.1   -0.9   1   0.240112    0.2     0.048   0
35.2   35.2   -0.8   1   0.335825    0.2   0.0672    0
35.3   35.3   -0.7   1   0.428183    0.2   0.0856    0
35.4   35.4   -0.7   1   0.516262    0.2   0.1033    0
35.5   35.5   -0.6   1   0.599183    0.2   0.1198    0
35.6   35.6   -0.5   1   0.676118    0.2   0.1352    0
35.7   35.7   -0.4   1   0.746297    0.2   0.1493    0
35.8   35.8   -0.3   1   0.809019    0.2   0.1618    0
35.9   35.9   -0.2   1   0.863657    0.2   0.1727    0
36     36     -0.1   1   0.909667    0.2   0.1819    0
36.1   36.1     -0   1   0.946587    0.2   0.1893    0
36.2   36.2   0.07   1   0.974049    0.2   0.1948    0
36.3   36.3   0.17   1   0.991779    0.2   0.1984    0
36.4   36.4   0.27   1   0.999599    0.2   0.1999    0
36.5   36.5   0.36   1   0.997432    0.2   0.1995    0
36.6   36.6   0.45   1   0.985298    0.2   0.1971    0
36.7   36.7   0.54   1    0.96332    0.2   0.1927    0
36.8   36.8   0.62   1   0.931717    0.2   0.1863    0
36.9   36.9    0.7   1   0.890804    0.2   0.1782    0
37     37     0.77   1   0.840991    0.2   0.1682    0
37.1   37.1   0.83   1   0.782775    0.2   0.1566    0
37.2   37.2   0.88   1   0.716737    0.2   0.1433    0
37.3   37.3   0.92   1   0.643538    0.2   0.1287    0
37.4   37.4   0.96   1   0.563909    0.2   0.1128    0
37.5   37.5   0.98   1   0.478646    0.2   0.0957    0
37.6   37.6      1   1      0.3886   0.2   0.0777    0
37.7   37.7      1   1   0.294672    0.2   0.0589    0
37.8   37.8   0.99   1   0.197799    0.2   0.0396    0
37.9   37.9   0.98   1    0.09895    0.2   0.0198    0
38     38     0.96   1   -0.00089    0.2   -2E-04    0
38.1   38.1   0.92   1 -0.10072 0.2   -0.02    0
38.2   38.2   0.88   1 -0.19954 0.2   -0.04    0
38.3   38.3   0.82   1 -0.29637 0.2 -0.059     0
38.4   38.4   0.76   1 -0.39024 0.2 -0.078     0
38.5   38.5    0.7   1   -0.4802 0.2 -0.096    0
38.6   38.6   0.62   1 -0.56538 0.2 -0.113     0
38.7   38.7   0.54   1   -0.6449 0.2 -0.129    0
38.8   38.8   0.45   1 -0.71797 0.2 -0.144     0
38.9   38.9   0.36   1 -0.78388 0.2 -0.157     0
39     39     0.27   1 -0.84195 0.2 -0.168     0
39.1   39.1   0.17   1 -0.89161 0.2 -0.178     0
39.2   39.2   0.07   1 -0.93236 0.2 -0.186     0
39.3   39.3     -0   1   -0.9638 0.2 -0.193    0
39.4   39.4   -0.1   1   -0.9856 0.2 -0.197    0
39.5   39.5   -0.2   1 -0.99756 0.2     -0.2   0
39.6   39.6   -0.3   1 -0.99955 0.2     -0.2   0
39.7   39.7   -0.4   1 -0.99155 0.2 -0.198     0
39.8   39.8   -0.5   1 -0.97365 0.2 -0.195     0
39.9   39.9   -0.6   1 -0.94601 0.2 -0.189     0
40     40     -0.7   1 -0.90893 0.2 -0.182     0
40.1   40.1   -0.7   1 -0.86276 0.2 -0.173     0
40.2   40.2   -0.8   1 -0.80797 0.2 -0.162     0
40.3   40.3   -0.9   1 -0.74511 0.2 -0.149     0
40.4   40.4   -0.9   1 -0.67481 0.2 -0.135     0
40.5   40.5   -0.9   1 -0.59776 0.2   -0.12    0
40.6   40.6     -1   1 -0.51474 0.2 -0.103     0
40.7   40.7     -1   1 -0.42658 0.2 -0.085     0
40.8   40.8     -1   1 -0.33415 0.2 -0.067     0
40.9   40.9     -1   1 -0.23839 0.2 -0.048     0
41     41       -1   1 -0.14024 0.2 -0.028     0
41.1   41.1     -1   1 -0.04069 0.2 -0.008     0
41.2   41.2   -0.9   1 0.059261 0.2 0.0119     0
41.3   41.3   -0.9   1 0.158623 0.2 0.0317     0
41.4   41.4   -0.8   1    0.2564               0
41.5   41.5   -0.8   1 0.351615                0
41.6   41.6   -0.7   1   0.443317    0
41.7   41.7   -0.7   1   0.530589    0
41.8   41.8   -0.6   1    0.61256    0
41.9   41.9   -0.5   1   0.688411    0
42     42     -0.4   1   0.757383    0
42.1   42.1   -0.3   1   0.818787    0
42.2   42.2   -0.2   1   0.872011    0
42.3   42.3   -0.1   1   0.916522    0
42.4   42.4     -0   1   0.951875    0
42.5   42.5   0.09   1   0.977717    0
42.6   42.6   0.19   1    0.99379    0
42.7   42.7   0.28   1   0.999934    0
42.8   42.8   0.38   1   0.996087    0
42.9   42.9   0.47   1   0.982287    0
43     43     0.56   1   0.958672    0
43.1   43.1   0.64   1   0.925479    0
43.2   43.2   0.71   1   0.883038    0
43.3   43.3   0.78   1   0.831775    0
43.4   43.4   0.84   1      0.7722   0
43.5   43.5   0.89   1   0.704911    0
43.6   43.6   0.93   1   0.630578    0
43.7   43.7   0.96   1   0.549944    0
43.8   43.8   0.98   1   0.463816    0
43.9   43.9      1   1   0.373053    0
44     44        1   1   0.278563    0
44.1   44.1   0.99   1   0.181289    0
44.2   44.2   0.98   1   0.082204    0
44.3   44.3   0.95   1     -0.0177   0
44.4   44.4   0.91   1   -0.11743    0
44.5   44.5   0.87   1   -0.21599    0
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1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
1   0
Second derivative
                                                             ACC
            -ab^2cos(bt+c)                                   /ACC/
                      -1     0      -0.2     0           1      1
             -0.9950042      0   -0.199      0         0.8    0.995
             -0.9800666      0   -0.196      0         0.6    0.98
             -0.9553365      0   -0.191      0         0.4    0.955
               -0.921061     0   -0.184      0         0.2    0.921
             -0.8775826      0   -0.176      0           0    0.878
             -0.8253356      0   -0.165    1.6    -0.0292     0.825
             -0.7648422      0   -0.153    1.6   -0.02336     0.765
             -0.6967067      0   -0.139    1.6   -0.01752     0.697
                -0.62161     0   -0.124    1.6   -0.01168     0.622
             -0.5403023      0   -0.108    1.6   -0.00584     0.54
             -0.4535961      0   -0.091    1.6           0    0.454
             -0.3623578      0   -0.072    3.2   -0.99829     0.362
             -0.2674988      0   -0.053    3.2   -0.79864     0.267
             -0.1699671      0   -0.034    3.2   -0.59898     0.17
             -0.0707372      0   -0.014    3.2   -0.39932     0.071
             0.02919952      0   0.0058    3.2   -0.19966     0.029
             0.12884449      0   0.0258    3.2           0    0.129
             0.22720209      0   0.0454    3.2           0    0.227
             0.32328957      0   0.0647                       0.323
             0.41614684      0   0.0832                       0.416
              0.5048461      0    0.101                       0.505
             0.58850112      0   0.1177                       0.589
             0.66627602      0   0.1333                       0.666
             0.73739372      0   0.1475                       0.737
             0.80114362      0   0.1602
             0.85688875      0   0.1714
             0.90407214      0   0.1808
0.94222234    0   0.1884
0.97095817    0   0.1942
 0.9899925    0    0.198
0.99913515    0   0.1998
0.99829478    0   0.1997
0.98747977    0   0.1975
0.96679819    0   0.1934
0.93645669    0   0.1873
0.89675842    0   0.1794
0.84810003    0   0.1696
0.79096771    0   0.1582
 0.7259323    0   0.1452
0.65364362    0   0.1307
0.57482395    0    0.115
0.49026082    0   0.0981
0.40079917    0   0.0802
0.30733287    0   0.0615
 0.2107958    0   0.0422
0.11215253    0   0.0224
0.01238866    0   0.0025
  -0.087499   0   -0.017
-0.1865124    0   -0.037
-0.2836622    0   -0.057
-0.3779777    0   -0.076
-0.4685167    0   -0.094
-0.5543743    0   -0.111
-0.6346929    0   -0.127
-0.7086698    0   -0.142
-0.7755659    0   -0.155
-0.8347128    0   -0.167
-0.8855195    0   -0.177
-0.9274784    0   -0.185
-0.9601703    0   -0.192
-0.9832684    0   -0.197
-0.9965421    0   -0.199
-0.9998586   0      -0.2
-0.9931849   0   -0.199
-0.9765876   0   -0.195
-0.9502326   0     -0.19
-0.9143831   0   -0.183
-0.8693975   0   -0.174
-0.8157251   0   -0.163
-0.7539023   0   -0.151
-0.6845467   0   -0.137
-0.6083513   0   -0.122
-0.5260775   0   -0.105
-0.4385473   0   -0.088
-0.3466353   0   -0.069
-0.2512598   0     -0.05
-0.1533739   0   -0.031
-0.0539554   0   -0.011
0.04600213   0   0.0092
0.14550003   0   0.0291
0.24354415   0   0.0487
0.33915486   0   0.0678
0.43137684   0   0.0863
0.51928865   0   0.1039
 0.6020119   0   0.1204
0.67872005   0   0.1357
0.74864665   0   0.1497
0.81109301   0   0.1622
0.86543521   0   0.1731
0.91113026   0   0.1822
 0.9477216   0   0.1895
0.97484362   0    0.195
0.99222533   0   0.1984
0.99969304   0   0.1999
0.99717216   0   0.1994
0.98468786   0   0.1969
0.96236488   0   0.1925
0.93042627    0   0.1861
0.88919115    0   0.1778
0.83907153    0   0.1678
0.78056818    0   0.1561
0.71426565    0   0.1429
0.64082642    0   0.1282
0.56098426    0   0.1122
0.47553693    0   0.0951
0.38533819    0   0.0771
0.29128928    0   0.0583
0.19432991    0   0.0389
0.09542885    0   0.0191
-0.0044257    0   -9E-04
  -0.104236   0    -0.021
-0.2030049    0    -0.041
-0.2997453    0     -0.06
-0.3934909    0    -0.079
-0.4833048    0    -0.097
-0.5682896    0    -0.114
-0.6475963    0     -0.13
-0.7204325    0    -0.144
-0.7860703    0    -0.157
  -0.843854   0    -0.169
-0.8932061    0    -0.179
-0.9336336    0    -0.187
-0.9647326    0    -0.193
-0.9861923    0    -0.197
-0.9977983    0       -0.2
-0.9994346    0       -0.2
-0.9910849    0    -0.198
-0.9728326    0    -0.195
   -0.94486   0    -0.189
-0.9074468    0    -0.181
-0.8609666    0    -0.172
  -0.805884   0    -0.161
-0.7427492    0   -0.149
-0.6721931    0   -0.134
-0.5949207    0   -0.119
  -0.511704   0   -0.102
-0.4233745    0   -0.085
-0.3308149    0   -0.066
-0.2349498    0   -0.047
-0.1367372    0   -0.027
-0.0371584    0   -0.007
0.06279172    0   0.0126
0.16211444    0   0.0324
0.25981736    0    0.052
0.35492427    0    0.071
0.44648489    0   0.0893
0.53358439    0   0.1067
0.61535248    0   0.1231
0.69097218    0   0.1382
0.75968791    0   0.1519
0.82081309    0   0.1642
0.87373698    0   0.1747
0.91793078    0   0.1836
0.95295292    0   0.1906
0.97845346    0   0.1957
0.99417763    0   0.1988
0.99996829    0       0.2
0.99576761    0   0.1992
0.98161754    0   0.1963
0.95765948    0   0.1915
 0.9241328    0   0.1848
0.88137249    0   0.1763
 0.8298058    0    0.166
0.76994796    0    0.154
0.70239706    0   0.1405
0.62782804    0   0.1256
0.54698596    0   0.1094
0.46067859    0 0.0921
0.36976826    0 0.074
0.27516334    0 0.055
0.17780907    0 0.0356
0.07867819    0 0.0157
-0.0212388    0 -0.004
-0.1209436    0 -0.024
   -0.21944   0 -0.044
-0.3157438    0 -0.063
-0.4088927    0 -0.082
-0.4979562    0    -0.1
-0.5820443    0 -0.116
-0.6603167    0 -0.132
-0.7319915    0 -0.146
-0.7963525    0 -0.159
-0.8527566    0 -0.171
-0.9006402    0   -0.18
-0.9395249    0 -0.188
-0.9690222    0 -0.194
-0.9888373    0 -0.198
-0.9987724    0    -0.2
  -0.998728   0    -0.2
-0.9887046    0 -0.198
-0.9688025    0 -0.194
-0.9392203    0 -0.188
-0.9002539    0   -0.18
-0.8522923    0   -0.17
  -0.795815   0 -0.159
-0.7313861    0 -0.146
-0.6596495    0 -0.132
-0.5813218    0 -0.116
-0.4971858    0 -0.099
-0.4080821    0 -0.082
-0.3149009    0 -0.063
-0.2185734    0 -0.044
-0.1200619    0   -0.024
-0.0203508    0   -0.004
0.07956357    0   0.0159
0.17868301    0   0.0357
 0.2760171    0   0.0552
0.37059333    0   0.0741
 0.4614667    0   0.0923
0.54772926    0   0.1095
0.62851909    0   0.1257
0.70302896    0   0.1406
 0.7705144    0   0.1541
0.83030111    0   0.1661
0.88179173    0   0.1764
0.92447177    0   0.1849
0.95791481    0   0.1916
0.98178667    0   0.1964
0.99584884    0   0.1992
0.99996083    0       0.2
0.99408153    0   0.1988
 0.9782697    0   0.1957
0.95268332    0   0.1905
0.91757805    0   0.1835
0.87330464    0   0.1747
0.82030546    0   0.1641
0.75911006    0   0.1518
0.69032988    0   0.1381
0.61465215    0   0.1229
0.53283302    0   0.1066
    0.44569   0   0.0891
0.35409379    0   0.0708
 0.2589596    0   0.0518
0.16123796    0   0.0322
0.06190529    0   0.0124
-0.0380459    0   -0.008
  -0.137617   0   -0.028
  -0.235813   0    -0.047
-0.3316529    0    -0.066
  -0.424179   0    -0.085
-0.5124669    0    -0.102
-0.5956343    0    -0.119
-0.6728504    0    -0.135
-0.7433436    0    -0.149
-0.8064095    0    -0.161
  -0.861418   0    -0.172
-0.9078196    0    -0.182
-0.9451505    0    -0.189
-0.9730378    0    -0.195
-0.9912028    0    -0.198
-0.9994641    0       -0.2
  -0.997739   0       -0.2
-0.9860448    0    -0.197
-0.9644984    0    -0.193
-0.9333151    0    -0.187
-0.8928064    0    -0.179
-0.8433771    0    -0.169
  -0.785521   0    -0.157
-0.7198162    0    -0.144
-0.6469193    0    -0.129
-0.5675586    0    -0.114
  -0.482527   0    -0.097
-0.3926742    0    -0.079
-0.2988979    0     -0.06
-0.2021351    0     -0.04
-0.1033527    0    -0.021
-0.0035375    0   -7E-04
0.09631292    0   0.0193
0.19520105    0     0.039
0.29213881    0   0.0584
0.38615761    0   0.0772
0.47631805    0   0.0953
0.56171928    0   0.1123
0.64150799    0   0.1283
0.71488697    0    0.143
0.78112303    0   0.1562
0.83955437    0   0.1679
0.88959717    0   0.1779
 0.9307514    0   0.1862
0.96260587    0   0.1925
 0.9848423    0    0.197
0.99723851    0   0.1994
0.99967064    0   0.1999
 0.9921144    0   0.1984
0.97464528    0   0.1949
0.94743782    0   0.1895
0.91076388    0   0.1822
0.86498988    0    0.173
 0.8105732    0   0.1621
0.74805753    0   0.1496
0.67806752    0   0.1356
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