## [SHM review questions]

1. A vertical block-spring system on earth has a period of 6.0 s. What is the period of this

same system on the moon where the acceleration due to gravity is roughly 1/6 that of

earth?

(a) 1.0 s (c) 6.0 s (e) 36 s

(b) 2.4 s (d) 15 s

2. Which one of the following statements is true concerning an object executing simple

harmonic motion?

(a) Its velocity is never zero.

(b) Its acceleration is never zero.

(c) Its velocity and acceleration are simultaneously zero.

(d) Its velocity is zero when its acceleration is a maximum.

(e) Its maximum acceleration is equal to its maximum velocity.

3. When a force of 20.0 N is applied to a spring, it elongates 0.20 m. Determine the

period of oscillation of a 4.0-kg object suspended from this spring.

(a) 0.6 s (c) 3.1 s (e) 6.3 s

(b) 1.3 s (d) 4.1 s

4. A ball hung from a vertical spring oscillates in simple harmonic motion with an

angular frequency of 2.6 rad/s and an amplitude of 0.075 m. What is the maximum

acceleration of the ball?

(a) 0.13 m/s2 (c) 0.51 m/s2 (e) 35 m/s2

(b) 0.20 m/s2 (d) 2.6 m/s2

5. The acceleration of a certain simple harmonic oscillator is given by

a = -(15.8 m/s2) cos (2.51t).

What is the amplitude of the simple harmonic motion?

(a) 2.51 m (c) 6.30 m (e) 15.8 m

(b) 4.41 m (d) 11.1 m

6. A 1.0-kg object is suspended from a spring with k = 16 N/m. The mass is pulled 0.25 m

downward from its equilibrium position and allowed to oscillate. What is the maximum

kinetic energy of the object?

(a) 0.25 J (c) 1.0 J (e) 4.0 J

(b) 0.50 J (d) 2.0 J

7. 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 (c) 0.8 J (e) 4 J

(b) 0.6 J (d) 2 J

8. A certain spring compressed 0.20 m has 10 J of elastic potential energy. The spring is

then cut into two halves and one of the halves is compressed by 0.20 m. How much

potential energy is stored in the compressed half of the spring?

(a) 5 J (c) 14 J (e) 40 J

(b) 10 J (d) 20 J

9. A 10-kg box is at rest at the end of an unstretched

spring with constant k = 4000 N/m. The mass is

struck with a hammer giving it a velocity of 6.0 m/s

to the right across a frictionless surface. What is the

amplitude of the resulting oscillation of this system?

(a) 0.3 m (d) 0.6 m

(b) 0.4 m (e) 2 m

(c) 0.5 m

10. A 1.0-kg block oscillates with a frequency of 10 Hz at the end of a certain spring. The

spring is then cut into two halves. The 1.0-kg block is then made to oscillate at the

end of one of the halves. What is the frequency of oscillation of the block?

(a) 5 Hz (c) 14 Hz (e) 40 Hz

(b) 10 Hz (d) 20 Hz

11. The spring constant for the spring in a special cannon is 1800 N/m. In cocking the

cannon, the spring is compressed 0.55 m. What is the initial speed of a 7.0-kg

cannonball at rest on the free end of the spring when it is released?

(a) 77 m/s (c) 12 m/s (e) 16 m/s

(b) 140 m/s (d) 8.8 m/s

12. A pendulum is transported from sea-level, where the acceleration due to gravity g =

9.80 m/s2, to the bottom of Death Valley. At this location, the period of the pendulum

is decreased by 3.00%. What is the value of g in Death Valley?

(a) 9.22 m/s2 (c) 9.80 m/s2 (e) 10.4 m/s2

(b) 9.51 m/s2 (d) 10.1 m/s2

13. In a certain clock, a pendulum of length L1 has a period T1 = 0.95 s. The length of the

pendulum is adjusted to a new value L2 such that T2 = 1.0 s. What is the ratio L2/L1?

(a) 0.90 (c) 1.0 (e) 1.3

(b) 0.95 (d) 1.1

14. What is the period of a pendulum consisting of a 6-kg object oscillating on a 4-m

string?

(a) 0.25 s (c) 1.0 s (e) 4.0 s

(b) 0.50 s (d) 2.0 s

15. A simple pendulum consists of a ball of mass m suspended from the ceiling using a

string of length L. The ball is displaced from its equilibrium position by an angle _.

What is the magnitude of the restoring force that moves the ball toward its

equilibrium position and produces simple harmonic motion?

(a) kx (c) mg (cos θ) (e) mgL(sin θ)

(b) mg (d) mg (sin θ)

16. A simple pendulum on earth has a period of 6.0 s. What is the approximate period of

this pendulum on the moon where the acceleration due to gravity is roughly 1/6 that

of earth?

(a) 1.0 s (c) 6.0 s (e) 36 s

(b) 2.4 s (d) 15 s

17. A thin, circular hoop with a radius of 0.22 m is hanging on a nail. Adam notices that

the hoop is oscillating back and forth through small angles like a physical pendulum.

The moment of inertia of the hoop for the rotational axis passing through the nail

is I = 2mr2. What is the period of the hoop?

(a) 0.21 s (c) 0.59 s (e) 1.3 s

(b) 0.42 s (d) 0.94 s

1. c

2. d

3. b

4. c

5. a

6. b

7. c

8. d

9. a

10. c

11. d

12. e

13. d

14. e

15. d

16. d

17. e

same system on the moon where the acceleration due to gravity is roughly 1/6 that of

earth?

(a) 1.0 s (c) 6.0 s (e) 36 s

(b) 2.4 s (d) 15 s

2. Which one of the following statements is true concerning an object executing simple

harmonic motion?

(a) Its velocity is never zero.

(b) Its acceleration is never zero.

(c) Its velocity and acceleration are simultaneously zero.

(d) Its velocity is zero when its acceleration is a maximum.

(e) Its maximum acceleration is equal to its maximum velocity.

3. When a force of 20.0 N is applied to a spring, it elongates 0.20 m. Determine the

period of oscillation of a 4.0-kg object suspended from this spring.

(a) 0.6 s (c) 3.1 s (e) 6.3 s

(b) 1.3 s (d) 4.1 s

4. A ball hung from a vertical spring oscillates in simple harmonic motion with an

angular frequency of 2.6 rad/s and an amplitude of 0.075 m. What is the maximum

acceleration of the ball?

(a) 0.13 m/s2 (c) 0.51 m/s2 (e) 35 m/s2

(b) 0.20 m/s2 (d) 2.6 m/s2

5. The acceleration of a certain simple harmonic oscillator is given by

a = -(15.8 m/s2) cos (2.51t).

What is the amplitude of the simple harmonic motion?

(a) 2.51 m (c) 6.30 m (e) 15.8 m

(b) 4.41 m (d) 11.1 m

6. A 1.0-kg object is suspended from a spring with k = 16 N/m. The mass is pulled 0.25 m

downward from its equilibrium position and allowed to oscillate. What is the maximum

kinetic energy of the object?

(a) 0.25 J (c) 1.0 J (e) 4.0 J

(b) 0.50 J (d) 2.0 J

7. 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 (c) 0.8 J (e) 4 J

(b) 0.6 J (d) 2 J

8. A certain spring compressed 0.20 m has 10 J of elastic potential energy. The spring is

then cut into two halves and one of the halves is compressed by 0.20 m. How much

potential energy is stored in the compressed half of the spring?

(a) 5 J (c) 14 J (e) 40 J

(b) 10 J (d) 20 J

9. A 10-kg box is at rest at the end of an unstretched

spring with constant k = 4000 N/m. The mass is

struck with a hammer giving it a velocity of 6.0 m/s

to the right across a frictionless surface. What is the

amplitude of the resulting oscillation of this system?

(a) 0.3 m (d) 0.6 m

(b) 0.4 m (e) 2 m

(c) 0.5 m

10. A 1.0-kg block oscillates with a frequency of 10 Hz at the end of a certain spring. The

spring is then cut into two halves. The 1.0-kg block is then made to oscillate at the

end of one of the halves. What is the frequency of oscillation of the block?

(a) 5 Hz (c) 14 Hz (e) 40 Hz

(b) 10 Hz (d) 20 Hz

11. The spring constant for the spring in a special cannon is 1800 N/m. In cocking the

cannon, the spring is compressed 0.55 m. What is the initial speed of a 7.0-kg

cannonball at rest on the free end of the spring when it is released?

(a) 77 m/s (c) 12 m/s (e) 16 m/s

(b) 140 m/s (d) 8.8 m/s

12. A pendulum is transported from sea-level, where the acceleration due to gravity g =

9.80 m/s2, to the bottom of Death Valley. At this location, the period of the pendulum

is decreased by 3.00%. What is the value of g in Death Valley?

(a) 9.22 m/s2 (c) 9.80 m/s2 (e) 10.4 m/s2

(b) 9.51 m/s2 (d) 10.1 m/s2

13. In a certain clock, a pendulum of length L1 has a period T1 = 0.95 s. The length of the

pendulum is adjusted to a new value L2 such that T2 = 1.0 s. What is the ratio L2/L1?

(a) 0.90 (c) 1.0 (e) 1.3

(b) 0.95 (d) 1.1

14. What is the period of a pendulum consisting of a 6-kg object oscillating on a 4-m

string?

(a) 0.25 s (c) 1.0 s (e) 4.0 s

(b) 0.50 s (d) 2.0 s

15. A simple pendulum consists of a ball of mass m suspended from the ceiling using a

string of length L. The ball is displaced from its equilibrium position by an angle _.

What is the magnitude of the restoring force that moves the ball toward its

equilibrium position and produces simple harmonic motion?

(a) kx (c) mg (cos θ) (e) mgL(sin θ)

(b) mg (d) mg (sin θ)

16. A simple pendulum on earth has a period of 6.0 s. What is the approximate period of

this pendulum on the moon where the acceleration due to gravity is roughly 1/6 that

of earth?

(a) 1.0 s (c) 6.0 s (e) 36 s

(b) 2.4 s (d) 15 s

17. A thin, circular hoop with a radius of 0.22 m is hanging on a nail. Adam notices that

the hoop is oscillating back and forth through small angles like a physical pendulum.

The moment of inertia of the hoop for the rotational axis passing through the nail

is I = 2mr2. What is the period of the hoop?

(a) 0.21 s (c) 0.59 s (e) 1.3 s

(b) 0.42 s (d) 0.94 s

**Answer Key**1. c

2. d

3. b

4. c

5. a

6. b

7. c

8. d

9. a

10. c

11. d

12. e

13. d

14. e

15. d

16. d

17. e