# Language of physics MCQ - DOC - DOC

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```					                                         Oscillations MCQ

Simple Harmonic Motion

Question H1: Why study this stuff?
Simple harmonic motion (SHM) is a technical term used to describe a certain kind of idealised
oscillation. Practically all the oscillations that one can see directly in the natural world are much
more complicated than SHM. Why then do physicists make such a big deal out of studying SHM?
A:    It is the only kind of oscillation that can be described mathematically.
B*: Any real oscillation can be analysed as a superposition (sum or integral) of SHMs with
different frequencies.
C:    Physics is concerned mainly with the unnatural world.
D:    Students are too stupid to appreciate the real world.
E:    It is good torture for students.
Feedback:
You should be able to get answer B because it is meant to look like the only sensible statement on
the list. However the question itself is not so silly. If you understand SHM you have progressed a
long way towards understanding all kinds of oscillations. This is one of the typical things about
physics that make physicists think that it is an easy subject; if you understand simple idealised
things like SHM then you understand a helluva lot.

Question H2:
Simple harmonic motion (SHM) is a technical term used to describe a certain kind of idealised
oscillation.
A simple harmonic oscillation has
A*: fixed frequency and fixed amplitude.
B:    fixed frequency and variable amplitude.
C:    variable frequency and fixed amplitude.
D:    variable frequency and variable amplitude.
?:    Don't know.
Feedback:
In the idealised world where one can talk about a simple harmonic motion, the SHM goes on
repeating itself exactly forever. Since it takes only one value of frequency to specify the motion, that
frequency must be unchanged. Also, in the idealised world, since the motion repeats itself exactly
the amplitude must also be constant. Mathematically SHM can be described by a sine function
multiplied by a constant (the amplitude). The sine function is one of those functions which repeats
indefinitely; cosine will do just as well.

Question H3:
A simple harmonic oscillation of a given system can be specified completely by stating its
A*: amplitude, frequency and initial phase.
B:    amplitude, frequency and wavelength.
C:    frequency and wavelength.
D:    frequency, wavelength and initial phase.
?:    Don't know.
Feedback:
This follows from the previous question and answer. Two SHMs with the same amplitude and
frequency could differ by being out of step with each other. The other alternatives can be ruled out
because they all mention wavelength, a concept which has no meaning in relation to a single
oscillation.

Question H4:
We can't get very far in talking about SHM without doing a little mathematics, so it its important to
be able to recognise some equations which can represent SHM.
In the equations below, A, B,  and are constants; y and t are variables; t represents time.
Only one of the following equations does not represent SHM. Which one is that?
A:      Asin(t)
y
B:              
  Bcos( t)
y
C:      Asin(t)  Bcos(t)
y
D:      Asin(t  )
y
E*:   Asin(t)  Bcos(2t)
y
?:  Don't know.
Feedback:
The graphs of the first four equations all have the same shape and frequency; they differ only in
their initial phases. The last equation has terms with two different frequencies, one of which is
double the other, so it cannot be SHM. It is the sum of two different SHMs.

This is just a question about names. This equation represents a SHM:
  Asin(t  ) .
y
Which part of the expression on the right hand side is called the phase?
A:    Asin(t  )

B:     t  )
sin(

C*:  t  

D: 
E:    A
Feedback:
There is not much argument behind trivia questions. The answers are usually just matters of
definition or convention. Some people might pick answer D, . The name for that is phase
constant, or more meaningfully, initial phase, meaning the value of the phase when the time
variable is zero. It is part of the expression for phase.
Extra:
The alternative name of "phase angle" for suggested by Halliday, Resnick & Walker (edition 5,
page 374) is silly; since  is no more or less an "angle" than t is an angle. Referring to phase as an
angle is potentially misleading because it seems to suggest that phase is related to directions in
space or angles between lines whereas it is really just a dimensionless variable (with no units) that is
the argument of the sin or cos function. It is not necessary, therefore to gratuitously add the unit
radian to values of phase. The habit of calling it an angle seems to derive from the practice of
drawing diagrams of a rotating radius as an aid to calculation of phase. Similarly, the unit of angular
frequency is really the reciprocal second, not radian per second.
Question H7:
Here is a displacement-time graph of an object moving with simple harmonic motion. What is the
frequency of the SHM?

A*: 0.40 Hz
B:    1.25 Hz
C:    2.50 Hz
D:    5.00 Hz
?:    Don't know.
Feedback:
To find the frequency we first need to find the period. To do that look for a number of complete
oscillations on the graph. The first peak occurs at 0.25 s and the third peak occurs at 5.25 s. That's
two complete oscillations in 5.0 s. So the period is 2.5 s. The frequency is the reciprocal of that:
0.40 s-1 or 0.40 Hz.
Extra:
conveniently possible. That's why the answer was worked out using two oscillations rather than one.

Question H8:
Here is the same graph again.
What is the amplitude of this motion?
A:   4.0 cm.
B:   5.0 cm.
C:   8.0 cm.
D:   10.0 cm
?:   Don't know.
Feedback:
The amplitude is the magnitude of the biggest displacement from the mid-point or equilibrium
position.
Extra:
An alternative way of describing how big the oscillation is would be to quote the value of the
difference between the extreme points, 10.0 cm; the name sometimes given to that value is peak-to-
peak amplitude.

Question H9:
Here is a displacement-time graph of an object which is not moving with simple harmonic motion.
But it is still an oscillation and it has a period.

Estimate that period.
A:   0.25 s.
B:    0.3 s.
C:    0.5 s.
D:    0.7 s
E:    1.0 s.
F*:   2.0 s
?:    Don't know.
Feedback:
The period of any oscillation is the time interval required for one complete cycle of the whole
pattern. Looking at this graph, the big positive peak occurs at 1.5 s, 3.5 s and 5.5 s with an exact
copy of the pattern in between those peaks. The pattern takes 2.0 s to repeat.
Extra:
There is clearly a subsidiary oscillation. In fact the graph was generated by adding two SHMs with
periods of 2.00 s and 0.67 s. If you picked answer D, you were probably looking at the second of
these two.

Question H10: Definition of SHM
It is possible to tell theoretically if a mechanical motion will be SHM through a careful analysis of
the forces in the system. An object will execute SHM with displacement coordinate x.
A:    all the forces involving x are conservative.
B*: the total force can be equated with -kx.
C:    all the forces involving x have equal and opposite reactions.
D:    the sum of all the forces involving x is zero.
E:    the total force on the object is always zero.
?:    Don't know.
Feedback:
Answer B is often used as a definition of SHM. Texts which do it that way then derive the equations
involving sin or cos functions as solutions of the equation of motion.
Extra:
Answer A is a necessary condition but it is not sufficient. If condition B is met then A should
follow. Answer C is true of all systems of forces - it is too general. Answer E leads to motion with
constant velocity.

Mechanical vibrations

Question M1:
Consider a thingy hanging from a spring. The system is set vibrating by pulling the thingy down
below its equilibrium position and then letting it go from rest.
The frequency of the oscillation is determined by
A:    the amount of the initial displacement
B*: the mass of the thingy and the properties of the spring
C:    the local gravitational field, g
D:    all of the above.
?:    Don't know.
Feedback:
The period and frequency of mechanical system depend only on the mechanical and elastic
properties of the system. We can be even more specific and say that the period is determined by two
properties of the system: inertia (mass) and elasticity. The relevant elastic property here is the spring
constant (k) which expresses the connection between restoring force and displacement. The mass
characterises the thing that is being acted upon by the force. Whether the oscillation is big or small
depends on how the system is treated, not on its innate properties, which excludes answer A. And
the gravitational field (answer D) is a property of the environment, not the system itself.

Question M2:
This is the same situation: a thingy oscillating on the end of a spring. The system is set vibrating by
pulling the thingy down below its equilibrium position and then letting it go from rest.

The amplitude of the oscillation is determined by
A*: the amount of the initial displacement.
B:    the mass of the thingy and the properties of the spring
C:    the local gravitational field, g.
D:    all of the above.
?:    Don't know.
Feedback:

Question M3:
We are still looking at the oscillating thingy hanging from a spring. The system was set vibrating by
pulling the thingy down below its equilibrium position and then letting it go from rest.

If the initial displacement is doubled what happens to the maximum kinetic energy of the
thingy?
A:    It is unchanged.
B:    It is doubled.
C*: It is increased by a factor of 4.
D:    We can't tell from the information provided.
?:    Don't know.
Feedback:
Maximum kinetic energy (KE) occurs when the thingy's speed is greatest and is proportional to the
square of that speed. The maximum speed, which occurs at the equilibrium point of the motion, is
given by Awhere A is amplitude and  is the angular frequency of the motion. Since  does not
depend on the initial displacement, its is a constant for a given system and doubling A results in a
doubling of the maximum speed, so the maximum KE goes up 4 times.

Question M4: Two things on springs
In their discussions of SHM text books sometimes consider a thingy attached to a horizontal spring
and moving horizontally on a frictionless surface, instead of the hanging thingy that we have been
looking at.
Suppose that the two springs and the two thingies are identical. Think about whether these two
systems are significantly different in other respects and decide which one of the following
statements is true.
A:    The systems have different periods because their motions are aligned differently with the
gravitational field.
B:    The hanging system has a slightly smaller period because the weight of the spring has to be
accounted for.
C:    The hanging system has a slightly larger period because the weight of the spring has to be
accounted for.
D*: The two systems have identical periods, no matter what the weight of the spring is.
?:    Don't know.
Feedback:
Neither the weight nor the mass of the spring makes a difference to the comparison. Although the
mass of the spring does make a difference and should be included in the analysis, its effect is the
same in both cases. Remember that in mechanical SHM only the mass and elastic properties of the
system matter. Gravity is irrelevant.
Extra:
In case you want to know, to correct for the mass of the spring add about a third of its value to that
of the thingy. Can you think of a reason why the fraction of the spring's mass added must less than
one?

Question M4: Simple pendulum
An object swinging on the end of a string forms a simple pendulum. Some students (and some texts)
often cite the simple pendulum's motion as an example of SHM. That is not quite accurate because
the motion is really
A*: approximately SHM only for small amplitudes.
B:    exactly SHM only for amplitudes that are smaller than a certain value.
C:    approximately SHM for all amplitudes.
?:    Don't know.
Feedback:
Anything that is an approximation can't be exact. Even for small amplitudes, SHM is only an
approximate model of the real motion. For large amplitudes, the approximation is so rough that one
does not use it. The thingy on the springy is a much better approximation to SHM.
Extra:
Another reason to be suspicious that pendulum motion is not truly SHM is the general rule about
mechanical SHM which says that the period depends on two properties of the system: inertia (mass)
and elasticity. The formula for the period of a pendulum contains neither of those factors!

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