Question 1

An angular simple harmonic oscillator is displaced 5.2 x 10-2 rad from its equilibrium position. If the torsion constant is 1200 N∙m/rad, what is the torque?

Accepted Answer

A)   12 N∙m
B)   23 N∙m
C)   43 N∙m
D)   52 N∙m
E)   62 N∙mF) C) and E)
G) A) and B)

Question 2

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 mF) B) and D)
G) C) and E)

Question 3

The displacement of an object oscillating on a spring is given by x(t)  = xmcos(   ω \omega ω t +  ϕ\phiϕ  ) . If the initial displacement is zero and the initial velocity is in the negative x direction, then the phase constant  ϕ\phiϕ   is:

Accepted Answer

A)   0 radians
B)     π\piπ /2 radians
C)     π\piπ  radians
D)   3  π\piπ /2 radians
E)   2  π\piπ  radians F) B) and C)
G) C) and D)

Question 4

Frequency f and angular frequency   ω \omega ω  are related by

Accepted Answer

A)   f =  π\piπ   ω \omega ω 
B)   f = 2  π\piπ   ω \omega ω 
C)   f =   ω \omega ω /  π\piπ 
D)   f =   ω \omega ω /2  π\piπ 
E)   f = 2  ω \omega ω /  π\piπF) A) and B)
G) A) and C)

Question 5

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, travelling toward the end point. The next time it is at the same place is:

Accepted Answer

A)   t = T
B)   t = T/2
C)   t = T/3
D)   t = T/4
E)   none of the aboveF) A) and C)
G) D) and E)

Question 6

For an oscillator subjected to a damping force proportional to its velocity:

Accepted Answer

A)   the displacement is a sinusoidal function of time
B)   the velocity is a sinusoidal function of time
C)   the frequency is a decreasing function of time
D)   the mechanical energy is constant
E)   none of the above is trueF) B) and D)
G) C) and E)

Question 7

A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m. If the system has an energy of 6.0 J, then the amplitude of the oscillation is:

Accepted Answer

A)   0.06 m
B)   0.17 m
C)   0.24 m
D)   4.9 m
E)   6.9 mF) B) and D)
G) C) and D)

Question 8

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 radF) A) and B)
G) A) and C)

Question 9

A sinusoidal force with a given amplitude is applied to an oscillator. To maintain the largest amplitude oscillation the frequency of the applied force should be:

Accepted Answer

A)   half the natural frequency of the oscillator
B)   the same as the natural frequency of the oscillator
C)   twice the natural frequency of the oscillator
D)   unrelated to the natural frequency of the oscillator
E)   determined from the maximum speed desiredF) All of the above
G) A) and E)

Question 10

A particle moves in simple harmonic motion according to x = 2cos(50t) , where x is in meters and t is in seconds. Its maximum velocity is:

Accepted Answer

A)   100 sin(50t)  m/s
B)   100 cos(50t)  m/s
C)   100 m/s
D)   200 m/s
E)   none of theseF) D) and E)
G) A) and E) C

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 energiesF) A) and C)
G) A) and E)

Question 12

Five particles undergo damped harmonic motion. Values for the spring constant k, the damping constant b, and the mass m are given below. Which leads to the smallest rate of loss of mechanical energy?

Accepted Answer

A)   k = 100 N/m, m = 50 g, b = 8 g∙m/s
B)   k = 150 N/m, m = 50 g, b = 5 g∙m/s
C)   k = 150 N/m, m = 10 g, b = 8 g∙m/s
D)   k = 200 N/m, m = 8 g, b = 6 g∙m/s
E)   k = 100 N/m, m = 2 g, b = 4 g∙m/sF) C) and D)
G) D) and E) B

Question 13

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 F) A) and B)
G) A) and E)

Question 14

A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m. If the oscillation is started by elongating the spring 0.15 m and giving the block a speed of 3.0 m/s, then the amplitude of the oscillation is:

Accepted Answer

A)   0.13 m
B)   0.18 m
C)   3.7 m
D)   5.2 m
E)   13 mF) B) and D)
G) B) and C)

Question 15

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

Accepted Answer

A)   amplitude
B)   frequency
C)   velocity
D)   displacement
E)   displacement squaredF) A) and E)
G) A) and D)

Question 16

In simple harmonic motion:

Accepted Answer

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 displacementF) A) and D)
G) D) and E)

Question 17

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

Accepted Answer

A)   has constant speed
B)   has varying amplitude
C)   has varying period
D)   has varying acceleration
E)   has varying massF) D) and E)
G) B) and D)

Question 18

The amplitude of any oscillator will be doubled by:

Accepted Answer

A)   doubling only the initial displacement
B)   doubling only the initial speed
C)   doubling the initial displacement and halving the initial speed
D)   doubling the initial speed and halving the initial displacement
E)   doubling both the initial displacement and the initial speedF) B) and C)
G) B) and E)

Question 19

An angular simple harmonic oscillator:

Accepted Answer

A)   oscillates at an angle to the x axis
B)   oscillates along the y axis
C)   involves an angular displacement and a restoring torque
D)   involves an angular displacement and a restoring force
E)   involves a linear displacement and a restoring torqueF) B) and C)
G) A) and E) C

Question 20

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:

Accepted Answer

A)   40 cm, 2 Hz
B)   20 cm, 4 Hz
C)   40 cm, 4 Hz
D)   25 cm, 4 Hz
E)   20 cm, 2 HzF) A) and E)
G) D) and E)

Exam 15: Oscillations

An angular simple harmonic oscillator is displaced 5.2 x 10-2 rad from its equilibrium position. If the torsion constant is 1200 N∙m/rad, what is the torque?

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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:

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The displacement of an object oscillating on a spring is given by x(t) = xmcos( ω \omega ω t + ϕ\phiϕ ) . If the initial displacement is zero and the initial velocity is in the negative x direction, then the phase constant ϕ\phiϕ is:

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Frequency f and angular frequency ω \omega ω are related by

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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, travelling toward the end point. The next time it is at the same place is:

Correct AnswerverifiedShow Answer

For an oscillator subjected to a damping force proportional to its velocity:

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A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m. If the system has an energy of 6.0 J, then the amplitude of the oscillation is:

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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?

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A sinusoidal force with a given amplitude is applied to an oscillator. To maintain the largest amplitude oscillation the frequency of the applied force should be:

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A particle moves in simple harmonic motion according to x = 2cos(50t) , where x is in meters and t is in seconds. Its maximum velocity is:

Correct AnswerverifiedC

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

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Five particles undergo damped harmonic motion. Values for the spring constant k, the damping constant b, and the mass m are given below. Which leads to the smallest rate of loss of mechanical energy?

Correct AnswerverifiedB

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

Correct AnswerverifiedShow Answer

A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m. If the oscillation is started by elongating the spring 0.15 m and giving the block a speed of 3.0 m/s, then the amplitude of the oscillation is:

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

In simple harmonic motion:

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

The amplitude of any oscillator will be doubled by:

Correct AnswerverifiedShow Answer

An angular simple harmonic oscillator:

Correct AnswerverifiedC

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:

Correct AnswerverifiedShow Answer

An angular simple harmonic oscillator is displaced 5.2 x 10^-2 rad from its equilibrium position. If the torsion constant is 1200 N∙m/rad, what is the torque?

Correct Answer
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The displacement of an object oscillating on a spring is given by x(t) = x_mcos( $\omega$ t + $\phi$ ) . If the initial displacement is zero and the initial velocity is in the negative x direction, then the phase constant $\phi$ is:

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Frequency f and angular frequency $\omega$ are related by

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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?

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C

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B

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

Correct Answer
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C

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