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Ch 10 Sample Multiple Choice Questions – Simple Harmonic Motion
Note : Unless otherwise noted, use g = 10 m/s2 and neglect air resistance.
Use the following to answer questions 1-3:
A block of mass m oscillates without friction on the end of a spring as shown above.
The minimum and maximum lengths of the spring as it oscillates are, respectively,
xmin and xmax. The graphs to the right can represent quantities associated with the
oscillation as functions of the length x of the spring.
1. Which graph can represent the total mechanical energy of the block-spring
system as a function of x?
(A) A
(B) B
(C) C
(D) D
(E) E
2.
Which graph can represent the kinetic energy of the block as a function of x?
(A) A
(B) B
(C) C
(D) D
(E) E
3.
Which graph can represent the magnitude of the force of the spring as a function
of x?
(A) A
(B) B
(C) C
(D) D
(E) E
Use the following to answer questions 4-7:
The equation which describes the motion of a mass oscillating on an ideal spring is
x = 6 cos 3t
where x is in centimeters and t is in seconds.
4. Which of the following statements is true for the oscillator at t = 0 ?
(A) The acceleration of the mass is zero.
(B) The net force on the mass is zero.
(C) The velocity of the mass is zero.
(D) The elastic potential energy of the mass is zero.
5.
The amplitude of the harmonic motion is
(A) 3 m
(B) 6 m
(C) 9 m
(D) 18 m
(E) 24 m
6.
The period of vibration for this mass on a spring is most nearly
(A) 1 s (B) 2 s (C) 3 s (D) 6 s (E) 9 s
7.
The total distance traveled by the mass during one full oscillation is
(A) 3 m
(B) 6 m
(C) 9 m
(D) 18 m
(E) 24 m
8.
A particle oscillates up and down in simple harmonic motion. Its height y as a function of time t is shown in the diagram
above. Which of the following is true for the velocity v and accleration a of the object at t = 3s?
(A) v = 0, a = 0
9.
(B) v > 0, a = 0
(C) v = 0, a < 0
(D) v > 0, a < 0
A spring required a force of 1.0 N to compress it 0.1 m. How much work is required to stretch the spring 0.4 m?
(A) 0.4 J
(B) 0.6 J
(C) 0.8 J
(D) 2 J
(E) 4 J
10. When an object is oscillating in simple harmonic motion in the vertical direction, its maximum speed occurs when the
object
(A) is at its highest point.
(B) is at the equilibrium point.
(C) is at the lowest point.
(D) has the maximum net force exerted on it.
Use the following to answer questions 11-16:
When a 0.20-kg block is suspended from a vertically hanging spring, the block stretches the spring from
its original length of 0.050 m to 0.060 m. The same block is attached to the same spring and placed on a
horizontal, frictionless surface. The block is then pulled so that the spring stretches to a total length of
0.10 m. The block is released at time t = 0 and undergoes simple harmonic motion.
11. What is the frequency of the motion?
(A) 0.50 Hz
(B) 1.0 Hz
(C) 5.0 Hz
(D) 10 Hz
(E) 31 Hz
12. Complete the following statement: In order to increase the frequency of the motion, one would have to
(A) reduce the spring constant.
(B) decrease the mass of the block on the end of the spring.
(C) reduce the distance that the spring is initially stretched. (D) increase the distance that the spring is initially stretched.
13. Which one of the following statements is true concerning the motion of the block?
(A) The magnitude of the acceleration is constant.
(B) The magnitude of the acceleration is greatest when the spring returns to the 5.0 cm position.
(C) The period of its motion depends on its amplitude.
(D) The magnitude of the velocity is greatest when the magnitude of the acceleration is greatest.
(E) The magnitude of the acceleration is greatest when the mass has reached its maximum displacement.
14. What is the speed of the block each time the spring is 5.0 cm long?
(A) zero
(B) 5.1 cm/s
(C) 16 cm/s
(D) 51 cm/s
(E) 160 cm/s
15. What is the maximum acceleration of the block?
(A) 1.6 m/s2
(B) 3.2 m/s2
(C) 50 m/s2
(D) 100 m/s2
(E) 160 m/s2
16. What is the total mechanical energy of the system at any instant?
(A) 0.25 J
(B) 0.50 J
(C) 1.0 J
(D) 5.0 J
(E) 10 J
Use the following to answer questions 17-18:
Two identical massless springs are hung from a horizontal support. A block of mass 5.0 kilograms is
suspended from the pair of springs, as shown right. When the block is in equilibrium, each spring is
stretched an additional 10 cm.
17. The force constant of each spring is most nearly
(A) 50 N/m
(B) 100 N/m
(C) 250 N/m
(D) 500 N/m
(E) 1000 N/m
18. When the block is set into oscillation, it has a frequency of f. Which of the following would be certain to increase f ?
(A) Increase the amplitude of the oscillations.
(B) Hang the block from only one of the springs and set in motion.
(C) Hang the block from the two springs connected in series and set in motion.
(D) Cut both springs in half and hang the block from the ends and set in motion.
(E) Hang a 10 kg block from the two springs and set in motion.
19. A 0.2-kg block is held in place by a force F that results in a 0.10-m compression of a spring beneath the
block. The spring constant is 100 N/m. Assuming the mass of the spring is negligible compared to that
of the block, to what maximum height would the block rise if the force F were removed?
(A) 0.25 m
(B) 0.50 m
(C) 2.5 m
(D) 5 m
(E) 10 m
20. As shown above, a spring of negligible mass and spring constant k is attached to the wall on one end, and the other end is
attached to the center of mass axis of a solid sphere of mass m and radius r (𝐼
= 𝑀𝑅 ). The spring
is stretched a distance A from equilibrium and let go. If the sphere freely rolls without slipping, what is the linear speed of
the center of mass of the sphere as it passes through the equilibrium position?
(A)
𝐴
(B)
𝐴
(C)
𝐴
(D)
𝐴
(E)
𝐴
21. A 2.0 kg box is traveling at 5.0 m/s on a smooth horizontal surface when it
collides with and sticks to a stationary 6.0 kg box. The larger box is attached to an
ideal spring of force constant (spring constant) 150 N/m, as shown in the figure.
What is the amplitude of the resulting oscillations?
(A) 0.14 m
(B) 0.29 m
(C) 0.58 m
(D) 1.0 m
(E) 1.2 m
22. A simple pendulum and a mass hanging on a spring both have a period of 1 s when set into small oscillatory motion on
Earth. They are taken to Planet X, which has the same diameter as Earth but twice the mass. Which of the following statements is true about the periods of the two objects on Planet X compared to their periods on Earth?
(A) Both are shorter.
(B) Both are the same.
(C) Both are longer.
(D) The period of the mass on the spring is shorter, that of the pendulum is the same.
(E) The period of the pendulum is shorter; that of the mass on the spring is the same.
23. A pendulum has simple harmonic motion provided that
(A) its bob is not too heavy.
(C) the arc through which it swings is not too small.
(B) the supporting string is not too long.
(D) the arc through which it swings is not too large.
24. Which of the following statements concerning the motion of a simple pendulum is incorrect?
(A) The kinetic energy is a minimum when the displacement is a maximum.
(B) The restoring force is a maximum when the displacement is a maximum.
(C) The time interval between conditions of maximum potential energy is one period.
(D) The velocity is a maximum when the restoring force is zero.
25. A giant simple pendulum has a period of 5.0 s. If the period is changed to 4.5 s, calculate the change in the length of the
string if g is constant at 9.81 m/s2.
(A) 1.2 m shorter (B) 0.8 m longer (C) 1.2 m longer (D) 0.8 m shorter (E) None of the above
26. An astronaut has landed on Planet N-40 and conducts an experiment to determine the acceleration due to gravity on that
planet. She uses a simple pendulum that is 0.640 m long and measures that 10 complete oscillations takes 26.0 s. What is
the acceleration of gravity on Planet N-40?
(A) 4.85 m/s2 (B) 1.66 m/s2 (C) 3.74 m/s2 (D) 2.39 m/s2 (E) 9.81 m/s2
Use the following to answer questions 27-30:
As shown in the figure right, a 0.50 kg bob swinging at the end of a string with negligible
mass undergoes simple harmonic motion. Various positions along the bob’s arc are labeled 1 thru 5. Point 3 is the lowest point of the swing and points 1 and 5 represent the
bob’s maximum displacement from the vertical. Neglect any frictional effects.
27. Which of the following statements concerning the bob’s motion is incorrect?
(A) The time it takes the bob to go from point 1 to point 2 is longer than the time it
takes the bob to go from point 2 to point 3.
(B) The increase in the bob’s kinetic energy from point 1 to point 2 is the same as its increase in kinetic energy from point 2 to point 3.
(C) The time it takes the bob to go from point 1 to point 3 is the same as the time it
takes the bob to go from point 3 to point 5.
(D) The kinetic energy of the bob at point 3 is equal to the work done on the bob by
gravity in moving from point 1 to point 3.
28. How long does it take the bob to swing from point 1 to point 5?
(A) 0.555 s (B) 1.11 s (C) 2.22 s (D) 3.33 s (E) 4.44 s
29. What is the speed of the bob at point 3?
(A) 0.308 m/s (B) 0.616 m/s (C) 4.55 m/s
30. What is the tension in the string a point 3?
(A) 4.8 N (B) 5.0 N (C) 5.2 N (D) 9.8 N
Answers
1. E
2. D
11. C 12. B
21. B 22. E
3. A
13. E
23. D
4. C
14. E
24. C
5. B
15. C
25. A
6. B
16. A
26. C
(D) 4.78 m/s
(E) 5.00 m/s
(E) 15 N
7. E
17. C
27. B
8. C
18. D
28. B
9. C
19. A
29. B
10. B
20. B
30. C