# Oscillations - Chapter No 14

Right Answers have been shown below in red color.

1. In simple harmonic motion, the restoring force must be proportional to the:

A. amplitude
B. frequency
C. velocity
D. displacement
E. displacement squared

2. An oscillatory motion must be simple harmonic if:

A. the amplitude is small
B. the potential energy is equal to the kinetic energy
C. the motion is along the arc of a circle
D. the acceleration varies sinusoidally with time
E. the derivative, dU/dx, of the potential energy is negative

3. In simple harmonic motion, the magnitude of the acceleration is:

A. constant
B. proportional to the displacement
C. inversely proportional to the displacement
D. greatest when the velocity is greatest
E. never greater than g

4. A particle is in simple harmonic motion with period T. At time t = 0 it is at the equilibrium point. Of the following times, at which time is it furthest from the equilibrium point?

A. 0.5T
B. 0.7T
C. T
D. 1.4T
E. 1.5T

5. A particle moves back and forth along the x axis from x = −xm to x = +xm, in simple harmonic motion with period T. At time t = 0 it is at x = +xm. When t = 0.75T:

A. it is at x = 0 and is traveling toward x = +xm
B. it is at x = 0 and is traveling toward x = −xm
C. it at x = +xm and is at rest
D. it is between x = 0 and x = +xm and is traveling toward x = −xm
E. it is between x = 0 and x = −xm and is traveling toward x = −xm

6. A particle oscillating in simple harmonic motion is:

A. never in equilibrium because it is in motion
B. never in equilibrium because there is always a force
C. in equilibrium at the ends of its path because its velocity is zero there
D. in equilibrium at the center of its path because the acceleration is zero there
E. in equilibrium at the ends of its path because the acceleration is zero there

7. An object is undergoing simple harmonic motion. Throughout a complete cycle it:

A. has constant speed
B. has varying amplitude
C. has varying period
D. has varying acceleration
E. has varying mass

8. When a body executes simple harmonic motion, its acceleration at the ends of its path must be:

A. zero
B. less than g
C. more than g
D. suddenly changing in sign
E. none of these

9. A particle is in simple harmonic motion with period T. At time t = 0 it is halfway between the equilibrium point and an end point of its motion, traveling toward the end point. The next time it is at the same place is:

A. t = T
B. t = T /2
C. t = T /4
D. t = T /8
E. none of the above

10. An object attached to one end of a spring makes 20 complete oscillations in 10 s. Its period is:

A. 2 Hz
B. 10 s
C. 0.5 Hz
D. 2 s
E. 0.50 s

11. An object attached to one end of a spring makes 20 vibrations in 10 s. Its frequency is:

A. 2 Hz
B. 10 s
C. 0.05 Hz
D. 2 s
E. 0.50 s

12. An object attached to one end of a spring makes 20 vibrations in 10 s. Its angular frequency is:

13. Frequency f and angular frequency ω are related by

A. f = πω
B. f = 2πω
C. f = ω/π
D. f = ω/2π
E. f = 2ω/π

13. Frequency f and angular frequency ω are related by

A. f = πω
B. f = 2πω
C. f = ω/π
D. f = ω/2π
E. f = 2ω/π

14. A block attached to a spring oscillates in simple harmonic motion along the x axis. The limits of its motion are x = 10 cm and x = 50 cm and it goes from one of these extremes to the other in 0.25 s. Its amplitude and frequency are:

A. 40 cm, 2 Hz
B. 20 cm, 4 Hz
C. 40 cm, 2 Hz
D. 25 cm, 4 Hz
E. 20 cm, 2 Hz

15. A weight suspended from an ideal spring oscillates up and down with a period T. If the amplitude of the oscillation is doubled, the period will be:

A. T
D. 1.5T
B. 2T
C. T /2
E. 4T

16. In simple harmonic motion, the magnitude of the acceleration is greatest when:

A. the displacement is zero
B. the displacement is maximum
C. the speed is maximum
D. the force is zero
E. the speed is between zero and its maximum

17. In simple harmonic motion, the displacement is maximum when the:

A. acceleration is zero
B. velocity is maximum
C. velocity is zero
D. kinetic energy is maximum
E. momentum is maximum

18. In simple harmonic motion:

A. the acceleration is greatest at the maximum displacement
B. the velocity is greatest at the maximum displacement
C. the period depends on the amplitude
D. the acceleration is constant
E. the acceleration is greatest at zero displacement

19. The amplitude and phase constant of an oscillator are determined by:

A. the frequency
B. the angular frequency
C. the initial displacement alone
D. the initial velocity alone
E. both the initial displacement and velocity

20. Two identical undamped oscillators have the same amplitude of oscillation only if:

A. they are started with the same displacement x0
B. they are started with the same velocity v0
C. they are started with the same phase
D. they are started so the combination ω2x02 + v02 is the same
E. they are started so the combination x2 + ω2v02 is the same