Question 1

A block on a spring is subjected to an applied sinusoidal force AND to a damping force that is proportional to its velocity.The energy dissipated by damping is supplied by:

Accepted Answer

A) the potential energy of the spring 
B) the kinetic energy of the mass 
C) gravity 
D) friction 
E) the applied force 
A) the potential energy of the spring 
B) the kinetic energy of the mass 
C) gravity 
D) friction 
E) the applied force E

Question 2

The angular frequency of a simple pendulum depends on its length and on the local acceleration due to gravity.The rate at which the angular displacement of the pendulum changes, dθ/dt, is:

Accepted Answer

A)    
B)    
C) 2π   
D)    
E) none of the above 
A)    
B)    
C) 2π   
D)    
E) none of the above E

Question 3

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

Accepted Answer

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 
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 B

Question 4

A simple pendulum has length L and period T.As it passes through its equilibrium position, the string is suddenly clamped at its mid-point.The period then becomes:

Accepted Answer

A) 2T 
B) T 
C) T/2 
D) T/4 
E) none of the above 
A) 2T 
B) T 
C) T/2 
D) T/4 
E) none of the above

Question 5

A simple harmonic oscillator consists of a mass m and an ideal spring with spring constant k.The particle oscillates as shown in (i)with period T.If the spring is cut in half and used with the same particle, as shown in (ii), the period will be:

Accepted Answer

A) 2T 
B)    
C)    
D) T 
E) T/2 
A) 2T 
B)    
C)    
D) T 
E) T/2

Question 6

Below are sets of values for the spring constant k, damping constant b, and mass m for a particle in damped harmonic motion.Which of the sets takes the longest time for its mechanical energy to decrease to one-fourth of its initial value?

Accepted Answer

A) A 
B) B 
C) C 
D) D 
E) E 
A) A 
B) B 
C) C 
D) D 
E) E

Question 7

Which of the following is NOT required for a simple pendulum undergoing simple harmonic oscillation?

Accepted Answer

A) a point mass 
B) a massless string 
C) a small amplitude 
D) gravitational force 
E) a large spring constant 
A) a point mass 
B) a massless string 
C) a small amplitude 
D) gravitational force 
E) a large spring constant

Question 8

The amplitude of oscillation of a simple pendulum is increased from 1$\degree$to 4$\degree$.Its maximum acceleration changes by a factor of:

Accepted Answer

A) 1/4 
B) 1/2 
C) 2 
D) 4 
E) 16 
A) 1/4 
B) 1/2 
C) 2 
D) 4 
E) 16

Question 9

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

Accepted Answer

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 
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

Question 10

A particle undergoes damped harmonic motion.The spring constant is 100 N/m; the damping constant is 8.0 x 10-3 kg∙m/s, and the mass is 0.050 kg.If the particle starts at its maximum displacement, x = 1.5 m, at time t = 0, what is the amplitude of the motion at t = 5.0 s?

Accepted Answer

A) 1.5 m 
B) 1.3 m 
C) 1.0 m 
D) 0.67 m 
E) 0.24 m 
A) 1.5 m 
B) 1.3 m 
C) 1.0 m 
D) 0.67 m 
E) 0.24 m

Question 11

It is impossible for two particles, each executing simple harmonic motion, to remain in phase with each other if they have different:

Accepted Answer

A) masses 
B) periods 
C) amplitudes 
D) spring constants 
E) kinetic energies 
A) masses 
B) periods 
C) amplitudes 
D) spring constants 
E) kinetic energies

Question 12

An object of mass m, oscillating on the end of a spring with spring constant k has amplitude A.Its maximum speed is:

Accepted Answer

A)    
B) A2k/m 
C)    
D) Am/k 
E) A2m/k 
A)    
B) A2k/m 
C)    
D) Am/k 
E) A2m/k

Question 13

An oscillator is driven by a sinusoidal force.The frequency of the applied force:

Accepted Answer

A) must be equal to the natural frequency of the oscillator 
B) becomes the natural frequency of the oscillator 
C) must be less than the natural frequency of the oscillator 
D) must be greater than the natural frequency of the oscillator 
E) is independent of the natural frequency of the oscillator 
A) must be equal to the natural frequency of the oscillator 
B) becomes the natural frequency of the oscillator 
C) must be less than the natural frequency of the oscillator 
D) must be greater than the natural frequency of the oscillator 
E) is independent of the natural frequency of the oscillator

Question 14

Both the x and y coordinates of a point execute simple harmonic motion.The result might be a circular orbit if:

Accepted Answer

A) the amplitudes are the same but the frequencies are different 
B) the amplitudes and frequencies are both the same 
C) the amplitudes and frequencies are both different 
D) the phase constants are the same but the amplitudes are different 
E) the amplitudes and the phase constants are both different 
A) the amplitudes are the same but the frequencies are different 
B) the amplitudes and frequencies are both the same 
C) the amplitudes and frequencies are both different 
D) the phase constants are the same but the amplitudes are different 
E) the amplitudes and the phase constants are both different

Question 15

A particle undergoes damped harmonic motion.The spring constant is 100 N/m; the damping constant is 8.0 x 10-3 kg∙m/s, and the mass is 0.050 kg.If the particle starts at its maximum displacement, x = 1.5 m, at time t = 0, what is the angular frequency of the oscillations?

Accepted Answer

A) 4.0 rad/s 
B) 8.0 rad/s 
C) 12 rad/s 
D) 23 rad/s 
E) 45 rad/s 
A) 4.0 rad/s 
B) 8.0 rad/s 
C) 12 rad/s 
D) 23 rad/s 
E) 45 rad/s

Question 16

The angular displacement of a simple pendulum is given by θ(t)= θm cos (ωt + φ).If the pendulum is 45 cm in length, and is given an angular speed dθ/dt = 3.4 rad/s at time t = 0, when it is hanging vertically, what is θm?

Accepted Answer

A) 4.6 rad 
B) 3.4 rad 
C) 1.4 rad 
D) 0.73 rad 
E) 0.45 rad 
A) 4.6 rad 
B) 3.4 rad 
C) 1.4 rad 
D) 0.73 rad 
E) 0.45 rad

Question 17

A 0.20-kg object mass attached to a spring whose spring constant is 500 N/m executes simple harmonic motion.If its maximum speed is 5.0 m/s, the amplitude of its oscillation is:

Accepted Answer

A) 0.0020 m 
B) 0.10 m 
C) 0.20 m 
D) 25 m 
E) 250 m 
A) 0.0020 m 
B) 0.10 m 
C) 0.20 m 
D) 25 m 
E) 250 m

Question 18

A disk whose rotational inertia is 450 kg∙m2 hangs from a wire whose torsion constant is 2300 N∙m/rad.What is the angular frequency of its torsional oscillations?

Accepted Answer

A) 0.20 rad/s 
B) 0.44 rad/s 
C) 1.0 rad/s 
D) 2.3 rad/s 
E) 5.1 rad/s 
A) 0.20 rad/s 
B) 0.44 rad/s 
C) 1.0 rad/s 
D) 2.3 rad/s 
E) 5.1 rad/s

Question 19

The acceleration of a body executing simple harmonic motion leads the velocity by what phase?

Accepted Answer

A) "0 rad 
B) "$\pi$/8 rad" 
C) "$\pi$/4 rad" 
D) "$\pi$/2 rad" 
E) "$\pi$ rad" 
A) "0 rad 
B) "$\pi$/8 rad" 
C) "$\pi$/4 rad" 
D) "$\pi$/2 rad" 
E) "$\pi$ rad"

Question 20

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

Accepted Answer

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

Exam 15: Oscillations

A block on a spring is subjected to an applied sinusoidal force AND to a damping force that is proportional to its velocity.The energy dissipated by damping is supplied by:

The angular frequency of a simple pendulum depends on its length and on the local acceleration due to gravity.The rate at which the angular displacement of the pendulum changes, dθ/dt, is:

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

A simple pendulum has length L and period T.As it passes through its equilibrium position, the string is suddenly clamped at its mid-point.The period then becomes:

A simple harmonic oscillator consists of a mass m and an ideal spring with spring constant k.The particle oscillates as shown in (i)with period T.If the spring is cut in half and used with the same particle, as shown in (ii), the period will be:

Below are sets of values for the spring constant k, damping constant b, and mass m for a particle in damped harmonic motion.Which of the sets takes the longest time for its mechanical energy to decrease to one-fourth of its initial value?

Which of the following is NOT required for a simple pendulum undergoing simple harmonic oscillation?

The amplitude of oscillation of a simple pendulum is increased from 1 °\degree° to 4 °\degree° .Its maximum acceleration changes by a factor of:

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

A particle undergoes damped harmonic motion.The spring constant is 100 N/m; the damping constant is 8.0 x 10-3 kg∙m/s, and the mass is 0.050 kg.If the particle starts at its maximum displacement, x = 1.5 m, at time t = 0, what is the amplitude of the motion at t = 5.0 s?

It is impossible for two particles, each executing simple harmonic motion, to remain in phase with each other if they have different:

An object of mass m, oscillating on the end of a spring with spring constant k has amplitude A.Its maximum speed is:

An oscillator is driven by a sinusoidal force.The frequency of the applied force:

Both the x and y coordinates of a point execute simple harmonic motion.The result might be a circular orbit if:

A particle undergoes damped harmonic motion.The spring constant is 100 N/m; the damping constant is 8.0 x 10-3 kg∙m/s, and the mass is 0.050 kg.If the particle starts at its maximum displacement, x = 1.5 m, at time t = 0, what is the angular frequency of the oscillations?

The angular displacement of a simple pendulum is given by θ(t)= θm cos (ωt + φ).If the pendulum is 45 cm in length, and is given an angular speed dθ/dt = 3.4 rad/s at time t = 0, when it is hanging vertically, what is θm?

A 0.20-kg object mass attached to a spring whose spring constant is 500 N/m executes simple harmonic motion.If its maximum speed is 5.0 m/s, the amplitude of its oscillation is:

A disk whose rotational inertia is 450 kg∙m2 hangs from a wire whose torsion constant is 2300 N∙m/rad.What is the angular frequency of its torsional oscillations?

The acceleration of a body executing simple harmonic motion leads the velocity by what phase?

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

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The amplitude of oscillation of a simple pendulum is increased from 1 $\degree$ to 4 $\degree$ .Its maximum acceleration changes by a factor of:

A particle undergoes damped harmonic motion.The spring constant is 100 N/m; the damping constant is 8.0 x 10^-3 kg∙m/s, and the mass is 0.050 kg.If the particle starts at its maximum displacement, x = 1.5 m, at time t = 0, what is the amplitude of the motion at t = 5.0 s?

A particle undergoes damped harmonic motion.The spring constant is 100 N/m; the damping constant is 8.0 x 10^-3 kg∙m/s, and the mass is 0.050 kg.If the particle starts at its maximum displacement, x = 1.5 m, at time t = 0, what is the angular frequency of the oscillations?

The angular displacement of a simple pendulum is given by θ(t)= θ_m cos (ωt + φ).If the pendulum is 45 cm in length, and is given an angular speed dθ/dt = 3.4 rad/s at time t = 0, when it is hanging vertically, what is θ_m?

A disk whose rotational inertia is 450 kg∙m² hangs from a wire whose torsion constant is 2300 N∙m/rad.What is the angular frequency of its torsional oscillations?