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PSI AP Physics C – Simple Harmonic Motion
Multiple Choice Questions (use g = 10 m/s2)
1. What is the period of a rotating or oscillating object?
(A) The time it takes for an object to complete one rotation or oscillation.
(B) How many times the object passes a specific point every second.
(C) The number of revolutions that an object completes in a given amount of time.
(D) How long it takes to make 2 complete revolutions or oscillations.
(E) Two times the frequency.
2. What is the frequency of a rotating or oscillating object?
(A) The time it takes for an object to complete one rotation or oscillation.
(B) The time it takes for an object to complete one half of a cycle.
(C) The inverse of the period of the object’s rotations or oscillations.
(D) One half of the period of the object’s rotations or oscillations.
(E) Two times the period of the object’s rotations or oscillations.
3. What is the period of an object that completes 5 oscillations in 30 seconds?
(A) 1/6 s
(B) 5 s
(C) 6 s
(D) 30 s
(E) 150 s
4. What is the frequency of an object that completes 64 oscillations in 16 seconds?
(A) 1/4 Hz
(B) 4 Hz
(C) 16 Hz
(D) 64 Hz
(E) 1024 Hz
5. If an object has a frequency of 0.25 Hz, what is its period?
(A) 1 s
(B) 2 s
(C) 4 s
(D) 0.5 s
(E) 0.25 s
6. If an object has a period of 8.00 s, what is its frequency?
(A) 0.0625 Hz
(B) 0.125 Hz
(C) 0.25 Hz
(D) 0.5 Hz
(E) 0.75 Hz
7. What is the term for the maximum displacement in Simple Harmonic Motion?
(A) Amplitude (B) Cycle (C) Period (D) Frequency (E) Equilibrium Point
8. An ideal spring has a spring constant K. If the spring was cut in half, what would be the
spring constant of each of the pieces?
(A) K/4
(B) K/2
(C) K
(D) 2K
(E) 4K
Problems 9-10
A 2 kg block is attached to a vertical un-stretched spring with a spring constant of 50 N/m, and
is released.
9. What is the amplitude of the object’s oscillation?
(A) 0.04 m
(B) 0.40 cm
(C) 40 cm
(D) 4 m
(E) 40 m
10. When will the object complete ¼ of a full cycle?
(A) 𝑡 = 2𝜋⁄5
(B) 𝑡 = 𝜋⁄5
(C) 𝑡 = 𝜋⁄10 (D) 𝑡 = 3𝜋⁄10 (E) 𝑡 = 𝜋
11. A spring on the earth is sent into Simple Harmonic Motion and has a period T. If that
same spring is brought to another planet with 1/5 the surface gravity, what will be the
new period?
(A) T/25
(B) T/5
(C) T
(D) 2T/5
(E) 5T
Problems 12-13
An object is undergoing Simple Harmonic Motion and its position is given by x = 2π cos (5t).
12. What is the amplitude of the object’s motion?
(A) 𝜋/4
(B) 𝜋/2
(C) 𝜋
(D) 2𝜋
(E) 4𝜋
13. At which of these points in time is the object at its amplitude?
(A) 0 s
(B) 𝜋/10 s
(C) 𝜋/8 s
(D) 𝜋/4 s
(E) 𝜋/2 s
Problems 14-16
Use the position-time graph below that describes the motion of an object.
14. What is the equation for the position of the object?
(A) 𝑥 = 2 cos (2𝜋𝑡)
𝜋
(B) 𝑥 = cos ( 2 𝑡)
𝜋
(C) 𝑥 = 2 sin ( 𝑡)
4
(D) 𝑥 = sin (2𝜋𝑡)
(E) 𝑥 = −2 sin (4𝜋𝑡)
15. What is the equation for the object’s velocity?
(A) 𝑣
(B) 𝑣
(C) 𝑣
(D) 𝑣
(E) 𝑣
𝜋
= 2 sin ( 4 𝑡)
= −2𝜋 sin (𝜋𝑡)
= −4 sin (2𝜋𝑡)
= −4𝜋 sin (2𝜋𝑡)
𝜋
= 2 cos ( 4 𝑡)
16. What is the acceleration of the object?
(A) 𝑎 = −4𝜋 sin (2𝜋𝑡)
(B) 𝑎 − 8 sin (2𝜋𝑡)
𝜋
(C) 𝑎 = −2 cos ( 4 𝑡)
𝜋
(D) 𝑎 = 2 sin ( 4 𝑡)
(E) 𝑎 = −8𝜋 2 cos (2𝜋𝑡)
Problems 17-19
A block with a mass of 4 kg is attached to a horizontal spring whose value of k is 64 N/m. The
block is displaced 50 cm from its initial position.
17. What is the total amount of energy stored in the spring?
(A) 16 J
(B) 8 J
(C) 32 J
(D) 2 J
(E) 4 J
18. What is the maximum velocity reached by the block?
(A) √2 𝑚/𝑠
(B) 2 m/s
(C) 2√2 𝑚/𝑠
(D) 4 m/s
(E) 6 m/s
19. What is the period of the block’s oscillation?
(A) π/4 s
(B) 3π/4 s
(C) π/2 s
(D) π s
(E) π/8 s
Problems 20-24
A pendulum is created by attaching a sphere to a string of length L and is held at an angle θ. The
sphere is then released.
L
θ
20. What is the sphere’s potential energy in terms of m, g, θ, and L as it swings?
(A) 𝑚𝑔𝐿
(B) 𝑚𝑔(𝐿 − 𝐿𝑠𝑖𝑛𝜃)
(C) 𝑚𝑔(𝐿 + 𝐿𝑠𝑖𝑛𝜃)
(D) 𝑚𝑔(𝐿 − 𝐿𝑐𝑜𝑠𝜃)
(E) 𝑚𝑔𝐿 − 𝐿𝑠𝑖𝑛𝜃
21. What is the sphere’s velocity in terms of m, g, θ, and L at the bottom of its path?
(A) 𝑣
(B) 𝑣
(C) 𝑣
(D) 𝑣
(E) 𝑣
= √2𝑔𝐿
= √2𝑔(𝐿 − 𝐿𝑠𝑖𝑛𝜃)
= √2𝑔(𝐿 + 𝐿𝑠𝑖𝑛𝜃)
= √2𝑔(𝐿 − 𝐿𝑐𝑜𝑠𝜃)
= √𝑔(𝐿 − 𝐿𝑐𝑜𝑠𝜃)
22. Which energy-position graph below shows the gravitational potential energy of the
sphere? The origin is the lowest point in the sphere’s swing.
23. What is the period of the pendulum in terms of m, g, θ, and L?
𝐿
(A) 2𝜋√𝑔
𝑔
(B) 𝜋√ 𝐿
(C)
𝜋
2
𝐿
√𝑔
(D)
1
2𝜋
𝑔
√𝐿
(E) 2𝜋√𝐿
24. What would happen to the period of the pendulum if it were moved to another planet
with a smaller value of surface gravitation?
(A) Nothing.
(B) The period would increase.
(C) The period would decrease.
(D) The period would oscillate between increasing and decreasing.
(E) Not enough information is given
m
m
25. A spring supports a mass m, which extends the spring a distance x as shown above and
to the left. If the spring was cut in half and both parts were used to hold up the mass in
parallel, as shown in the figure to the above and right, what would be the new x?
(A) x/4
(B) x/2
(C) x
(D) 2x
(E) 4x
26. An adjustable pendulum has a period of T when its length is L. You want it to have a
period of T/3. What would you adjust the length of the pendulum to?
(A) 9L
(B) 3L
(C) L/3
(D) L/9
(E) L/12
Problems 27-28
You create a physical pendulum by attaching an object with a mass of 5 kg to a pivot point
which is 25 cm away from the object’s center of gravity. The object has a moment of inertia of
50 kg/m2 about its pivot point, and is on the surface of the Earth.
27. What is the physical pendulum’s period as it oscillates about the pivot point?
(A) 𝜋⁄4
(B) 𝜋⁄2
(C) 𝜋
(D) 4𝜋
(E) 10𝜋
28. The physical pendulum is now brought to a planet with twice the surface gravity of
Earth. What is its period on the new planet?
(A) 2𝜋√2
(B) 2𝜋
(C) 𝜋√8
(D) 8𝜋
(E) 6𝜋
29. In a horizontal mass spring system, the maximum displacement is A. When is the
velocity the greatest?
(A) x = A
(B) x = -A
(C) x = 0
(D) x = A/2
(E) x = –A/2
30. For a simple pendulum, with no external forces acting on it, the total energy:
(A) decreases as the object falls.
(B) increases as the object falls.
(C) remains the same.
(D) is always zero.
(E) oscillates between increasing and decreasing.
31. In an experiment with a mass-spring oscillating system, measurements of the period are
made for different masses. When plotted on a graph, which of the following should
result in a straight-line fit of the measured data?
(A) T versus m
(B) T2 versus m
(C) T versus m2
(D) √𝑇 versus m
(E) √𝑇 versus m2
32. A mass-spring oscillating system undergoes SHM with a period T and amplitude A. If the
spring constant is k, which of the following is a possible expression for the kinetic energy
of the system as a function of time t?
1
2𝜋𝑡
(A) 𝐾𝐸 = 2 𝑚𝐴2 sin2 (
(B) 𝐾𝐸 =
(C) 𝐾𝐸 =
(D) 𝐾𝐸 = 𝑚𝐴 cos (
2
(E) 𝐾𝐸 =
)
𝑇
1
2
2 2𝜋𝑡
𝑘𝐴 sin ( 𝑇 )
2
1
2𝜋𝑡
2
𝑚𝐴
𝑠𝑖𝑛
(
)
2
𝑇
1
2
2 2𝜋𝑡
𝑇
2
2 2𝜋𝑡
𝑘𝐴 sin ( 𝑇 )
)
33. A mass-spring oscillating system undergoes SHM with amplitude A. At what location
from the equilibrium point will the kinetic energy of the system equal its potential
energy?
(A) x = A/2
(B) x = A/√2
(C) x = A/4
(D) x = A/3
(E) x = A/√3
34. A small mass is suspended at the end of a light string of length L that is attached to the
ceiling. The pendulum is placed closed to a nail, attached to a wall at a distance of 3L/4
from the ceiling that limits the pendulum swing. When the mass is displaced by a small
angle to point 1, and let go, moving to point 2, how long does it take to return to point
1?
(A)
(B)
3𝜋
2
7𝜋
4
𝐿
√𝑔
𝐿
√𝑔
3𝐿
(C) 𝜋√4𝑔
𝐿
(D) 𝜋√4𝑔
𝐿
(E) 𝜋√𝑔
35. A torsion pendulum has a disk with rotational inertia I that is suspended at the end of a
light elastic rod. When the disk is twisted by a small angle θ, the rod exerts a restoring
torque τ = -γθ, where γ is a constant. Which of the following differential equations
could be used to describe the pendulum motion?
(A)
(B)
(C)
(D)
(E)
𝑑2 𝜃
𝑑𝑡 2
𝑑𝜃
𝑑𝑡
= −𝜃
𝛾
=−𝐼𝜃
𝑑2 𝜃
𝑑𝑡 2
𝑑2 𝜃
𝑑𝑡 2
𝑑2 𝜃
𝑑𝑡 2
𝛾
= − 𝐼 𝜃2
𝐼
= −𝛾𝜃
𝛾
=−𝐼𝜃
PSI AP Physics C – Simple Harmonic Motion
Answer Key
1.A
2.C
3.C
4.B
5.C
6.B
7.A
8.D
9.C
10.C
11.C
12.D
13.A
14.A
15.D
16.E
17.B
18.B
19.C
20.D
21.D
22.A
23.A
24.B
25.A
26.D
27.D
28.A
29.C
30.C
31. B
32. B
33. B
34. A
35. E