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SHM-1. A ball bounces up and down on a floor with perfectly
elastic bounces, so that the ball bounces forever:
Is this an example of simple harmonic motion?
A) Yes
B) No
Answer: No. This motion has none of the characteristics of SHM. For instance, the restoring
force is mg, which is a constant, independent of the height. For SHM, you must have a restoring
force proportional to the displacement from equilibrium.
SHM-2. A mass is oscillating back and forth on a spring as shown. Position 0 is the equilibrium
position. No friction.
E
M 0
M
E
At Which position is the magnitude of the acceleration of the mass maximum?
A) 0
B) M
C) E
D) a is constant everywhere
At what position is the force on the mass a maximum?
A) 0
B) M
C) E
D) force is constant everywhere.
At what position is the total energy (PE + KE) a maximum?
A) 0
B) M
C) E
D) energy is constant everywhere.
Answers: The acceleration is maximum at position E. The force is max at position E. The total
energy is constant.
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SHM-3. A stiff spring and a floppy spring have potential energy diagrams shown below.
Which is the stiff spring? A) PINK
B) YELLOW
PE
PE
x
x
Pink
Yellow
Two masses are identical. One is attached to a stiff spring; the other to a floppy spring. Both are
positioned at x = 0 and given the same initial speeds. Which spring produces the largest
amplitude motion? A) The stiff spring
B) The floppy spring
C) Same!
Now the identical masses on the two different springs are pulled to the side and released from
rest with the same initial amplitude. Which spring produces the largest maximum speed of its
mass? A) The stiff spring
B The floppy spring C) Same!
If the spring constant is increased, but the total energy of a mass/spring system is kept constant,
what happens to the amplitude A of the motion?
A) A increases B) A decreases
C) A stays constant
Answers: The Yellow spring his the stiff one. The floppy spring will have the larger amplitude
motion, for a given initial speed of the mass starting at the origin. The stiff spring will have the
largest max speed, for a given initial amplitude, starting at rest. If the spring constant is
increased, but the total energy KE+PE is kept constant, then the amplitude decreases.
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SHM-4. The position of a mass on a spring as a function of time is shown below. When the
mass is at point P on the graph, ..
x
P
t
A) The velocity v > 0
A) The acceleration a > 0
B) v < 0
B) a < 0
C) v = 0
C) a = 0
Answers: The velocity is positive and the acceleration is negative.
d2x
 x.
SHM-5. Consider a variable x = x() and the differential equation
d2
Here are some proposed solutions of this equation:
I.
x  sin 
II.
x  cos 
How many of these are actually solutions:
A) all of them
B) None of them
D) 2 of them.
III.
x  e
C) 1 of them
Answer: 2 of them: I and II are solutions. III is not a solution.
SHM-6. A mass on a spring oscillates with a certain amplitude A and a certain period T. If the
mass m is doubled, the spring constant k of the spring is doubled, and the amplitude of motion A
is doubled, THEN the period T... A) increases
B) decreases C) stays the same.
Answer: The period T stays the same.
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SHM-7. The solid curve is a graph of
x( t )  A cos(t  )
x( t )  A cos(t ) . The dotted curve is a graph of
where  is a phase constant whose magnitude is less than /2. Is 
positive or negative?
x
A
t
-A
A: Positive
B: Negative.
[Hint: cos() reaches a maximum when =0, that is, at cos(0).]
Answer: Negative.
SHM-8. Consider the function f() = cos()
cos


What is  for one period?
A) 
B) 1 C) 2 D) 2
Answer: 2
E) T
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SHM-9. A mass on a spring oscillates with a certain amplitude A and a certain period T. If the
mass m is doubled, the spring constant k of the spring is doubled, and the amplitude of motion A
is doubled, THEN the period T...
A) increases B) decreases C) stays the same.
Answer: stays the same
SHM-10. What is the sign of cos(225o)? Sign of sin(225o)?
A) cos(225o) = (+) , sin(225o) = (–)
B) cos(225o) = (–) , sin(225o) = (+)
C) cos(225o) = (+) , sin(225o) = (+)
D) cos(225o) = (–) , sin(225o) = (–)
E) None of these. One of them is zero.
Answer: cos(225o) = (–) , sin(225o) = (–)
370o = (3/2). What is cos[(3/2)] and what is sin[(3/2)] ?
A) cos[(3/2)] = 1, sin[(3/2)] = 0
B) cos[(3/2)] = 0, sin[(3/2)] = 1
C) cos[(3/2)] = 1, sin[(3/2)] = 1
D) cos[(3/2)] = 0, sin[(3/2)] = 0
E) None of these
Answer: None of these: cos[(3/2)] = 0, sin[(3/2)] = 1
SHM-11.
A kid is swinging on a swing with a period T. A second kid climbs on with the first, doubling
the weight on the swing. The period of the swing is now...
A) the same, T
D) none of these.
B) 2T
C)
2T
Answer: the same T. The period of a simple pendulum depends only on g and the length of the
pendulum L.
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SHM-12.
You take your grandfather clock (a pendulum clock) to the Moon. On the Moon, does the clock
keep good time, or run slow or fast?
A) keeps good time B) runs slow C) runs fast
Answer: runs slow
SHM-13. The force on a pendulum mass along the direction of motion is mgsin.
For small , mgsinmg, and the period is independent
of amplitude. For larger amplitude motion, the period
A: increases
B: decreases
C: remains constant
Hint: does sin get bigger or smaller than  as 
increases.
mg
mgsin
Answer: For larger amplitude motion, the period increases