# 2011 Honors Vibrations and Waves

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2011 Honors Notes Chapter 13

Vibrations and Waves
1. How does the force on a spring is related to the distance a spring is stretched?

a. What is Hooke’s Law?

b. If a spring is cut in half, what happens to its spring constant?

c. If you know the force on the block below, how can you determine the
acceleration of the block? Is it constant?

d. For each of the pictures draw the force and acceleration directions. Label
the equilibrium point and the amplitude. In which picture is the force
maximum? Minimum?
2011 Honors Notes Chapter 13

2. What is the period of the motion?

a. Through what total distance does the block travel in one period?
A/2             A              2A              4A

3. What is the frequency of the motion?

4. The motion of Earth going around the Sun is
periodic with a period of 1 year. Is this motion
simple harmonic?

5. How is it possible to find the work done by a variable force?

a. What is the potential energy stored by a spring?
2011 Honors Notes Chapter 13

b. What does the potential energy change to as the block moves?

c. Is mechanical energy conserved in this system?

End

0

midpoint

0

End

0
Fill in the chart with constant, max or zero

Velocity     Kinetic      Potential    Force      Acceleration ETotal
Energy       energy
mid

End

6. Find the velocity as a function of the position.
2011 Honors Notes Chapter 13

7. A mass of 0.5 kg oscillates with amplitude of 0.2 meters on a
horizontal spring with spring constant of 100 N/m.
a. What is the total energy?

b. What is the velocity at a position of 0.1 meters from equilibrium?

8. A slingshot consists of a light leather cup, containing a stone that is pulled back
against two parallel rubber bands. It takes a force of 15 N to stretch either one of
these bands 1.0 cm.
a. What is the potential energy stored in the two bands together when a 50 g
stone is placed in the cup and pulled back 0.20 m from the equilibrium
position?

b. With what speed does the stone leave the slingshot?

9. At an outdoor market, a bunch of bananas is set into oscillatory motion with an
amplitude of 20.0 cm on a spring with a spring constant of 16.0 N/m. It is
observed that the maximum speed of the bunch of bananas is 40.0 cm/s. What is
the weight of the bananas in Newton’s?
2011 Honors Notes Chapter 13

10. Comparing simple harmonic motion with uniform circular motion

a. Draw a clock hand at 1 o’clock.

b. Draw a line from the end of the clock hand to the x axis. Describe the
motion of the point on the x-axis as the clock hand travels
counterclockwise.

c. Relate the amplitude (the length of the clock hand) of the motion to the
position of the point on the x axis.

d. Draw a graph of the position of the point on the x axis as a function of
time.
xmax
x
t

½T                 T
-xmax
-

e. Write the equation for the two motions given in class.
2011 Honors Notes Chapter 13

f. What if the blocks don’t travel at the same angular velocity?

g. Substitute angular displacement to relate to angular velocity/frequency.
Substitute in for angular velocity/frequency so that it is terms of period.

h. Write the equations for the two motions given in class.

i. What if the motion starts with an angular displacement?

j. Write the equations for the two motions given in class.
2011 Honors Notes Chapter 13

11. The position of a 0.2 kg object attached to a spring is described by
x= (0.5m) cos(0.5πt+π/2)
a. What is the position of the object at 2 seconds? At 0 seconds?

b. What is the spring constant?

c. What is the frequency?

12. Start with the velocity equation as a function of position. Find velocity as a
function of time.

a. Graph velocity as a function of time.

vmax
v
t

½T                 T
-vmax

13. How is angular velocity/frequency related to the spring constant and mass?
2011 Honors Notes Chapter 13

14. Find the period of simple harmonic motion.

15. Find the period of a simple pendulum.




16. A pendulum clock that works perfectly on Earth is taken to the Moon. Does it run
fast or slow there?
2011 Honors Notes Chapter 13

17. A simple pendulum is 5.00m long.
a. What is the period of simple harmonic motion for this pendulum if it is
located in an elevator accelerating upward at 5.00 m/s2?

b. What is the period if the elevator is accelerating downward at 5.00 m/s2?

18. What is a wave?

19. What is a medium?

20. What is an example of waves transferring energy?

21. Types of Waves
Mechanical Waves                         Electromagnetic waves
Mediums

What
oscillates?
Examples
2011 Honors Notes Chapter 13

22. Types of Mechanical Waves

Longitudinal Waves        Transverse waves
Mediums

Direction of
oscillations
Examples

23. Describing waves
a. Frequency

b. Amplitude

c. Wavelength

d. Wave speed

24. How are the terms above related?
2011 Honors Notes Chapter 13

25. In a long line of people waiting to buy tickets at a movie theater, when the first
person leaves, a pulse of motion occurs as people step forward to fill in the gap.
The gap moves through the line of people. What determines the speed of this
pulse? Is it transverse or longitudinal?

26. Speed of waves on strings

27. In mechanics, massless strings are often assumed. Why is this not a good
assumption when discussing waves on strings?

28. A simple pendulum consists of a ball of mass 5.00 kg hanging from a uniform
string of mass 0.060 kg and length L. If the period of oscillation for the pendulum
is 2.00s, determine the speed of a transverse wave in the string when the
pendulum hangs vertically.
2011 Honors Notes Chapter 13

29. Interference of Waves
a. Constructive interference

b. Destructive interference

30. Reflection of waves
a. What happens at a fixed end?

b. What happens at a free end?

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