Question 1

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

Accepted Answer

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

Question 2

A sinusoidal force with a given amplitude is applied to an oscillator. At resonance the amplitude of the oscillation is limited by:

Accepted Answer

A)   the damping force
B)   the initial amplitude
C)   the initial velocity
D)   the force of gravity
E)   none of the aboveF) B) and E)
G) C) and E)

Question 3

The amplitude of any oscillator can 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) A) and E)
G) None of the above

Question 4

Three physical pendulums, with masses m1, m2 = 2m1, and m3 = 3m1, have the same shape and size and are suspended at the same point. Rank them according to their periods, from shortest to longest.

Accepted Answer

A)   1, 2, 3
B)   3, 2, 1
C)   2, 3, 1
D)   2, 1, 3
E)   All the above are the sameF) A) and B)
G) B) and C) E

Question 5

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) B) and C)
G) A) and D)

Question 6

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

Accepted Answer

A)   acceleration is zero
B)   velocity is maximum
C)   velocity is zero
D)   kinetic energy is maximum
E)   momentum is maximumF) A) and B)
G) B) and C)

Question 7

An object on the end of a spring is set into oscillation by giving it an initial velocity while it is at its equilibrium position. In the first trial the initial velocity is v0 and in the second it is 4v0. In the second trial:

Accepted Answer

A)   the amplitude is half as great and the maximum acceleration is twice as great
B)   the amplitude is twice as great and the maximum acceleration is half as great
C)   both the amplitude and the maximum acceleration are twice as great
D)   both the amplitude and the maximum acceleration are four times as great
E)   the amplitude is four times as great and the maximum acceleration is twice as greatF) A) and B)
G) All of the above

Question 8

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

Accepted Answer

A)   f =   π\piπω \omega ω 
B)   f = 2  π\piπω \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) D) and E)

Question 9

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

Accepted Answer

A)   0.79 rad/s
B)   1.57 rad/s
C)   2.0 rad/s
D)   6.3 rad/s
E)   12.6 rad/sF) A) and D)
G) A) and E)

Question 10

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:

Accepted Answer

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 is 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 = -xmF) A) and B)
G) A) and D)

Question 11

A particle oscillating in simple harmonic motion is:

Accepted Answer

A)   never in equilibrium because it is in motion
B)   never in equilibrium because there is 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 thereF) C) and D)
G) All of the above D

Question 12

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
B)     π\piπ /2 radians
C)     π\piπ  radians
D)   3  π\piπ /2 radians
E)   2  π\piπ  radians F) D) and E)
G) All of the above

Question 13

A certain spring elongates 9 mm when it is suspended vertically and a block of mass M is hung on it. The natural frequency of this mass-spring system is:

Accepted Answer

A)   is 0.088 rad/s
B)   is 33 rad/s
C)   is 200 rad/s
D)   is 1140 rad/s
E)   cannot be computed unless the value of M is givenF) A) and E)
G) All of the above

Question 14

Both the x and y coordinates of a point execute simple harmonic motion. The frequencies are the same but the amplitudes are different. The resulting orbit might be:

Accepted Answer

A)   an ellipse
B)   a circle
C)   a parabola
D)   a hyperbola
E)   a squareF) C) and D)
G) D) and E)

Question 15

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) B) and C)

Question 16

The rotational inertia of a uniform thin rod about its end is ML2/3, where M is the mass and L is the length. Such a rod is hung vertically from one end and set into small amplitude oscillation. If L = 1.0 m this rod will have the same period as a simple pendulum of length:

Accepted Answer

A)   33 cm
B)   50 cm
C)   67 cm
D)   100 cm
E)   150 cmF) B) and D)
G) B) and C)

Question 17

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

Question 18

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

Accepted Answer

A)   0
B)     π\piπ /8 rad
C)     π\piπ /4 rad
D)     π\piπ /2 rad
E)     π\piπ  rad F) A) and C)
G) A) and B) D

Question 19

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

Accepted Answer

A)   0 and   π\piπ /2 radians
B)     π\piπ /2 and   π\piπ  radians
C)     π\piπ  and 3  π\piπ /2 radians
D)   3  π\piπ /2 and 2  π\piπ  radians
E)   none of the above ( ϕ\phiϕ  is exactly 0,   π\piπ /2,   π\piπ , or 3  π\piπ /2 radians)  F) A) and E)
G) C) and D)

Question 20

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

Exam 15: Oscillations

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

Correct AnswerverifiedShow Answer

A sinusoidal force with a given amplitude is applied to an oscillator. At resonance the amplitude of the oscillation is limited by:

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The amplitude of any oscillator can be doubled by:

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Three physical pendulums, with masses m1, m2 = 2m1, and m3 = 3m1, have the same shape and size and are suspended at the same point. Rank them according to their periods, from shortest to longest.

Correct AnswerverifiedE

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

Correct AnswerverifiedShow Answer

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

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An object on the end of a spring is set into oscillation by giving it an initial velocity while it is at its equilibrium position. In the first trial the initial velocity is v0 and in the second it is 4v0. In the second trial:

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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:

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A particle oscillating in simple harmonic motion is:

Correct AnswerverifiedD

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:

Correct AnswerverifiedShow Answer

A certain spring elongates 9 mm when it is suspended vertically and a block of mass M is hung on it. The natural frequency of this mass-spring system is:

Correct AnswerverifiedShow Answer

Both the x and y coordinates of a point execute simple harmonic motion. The frequencies are the same but the amplitudes are different. The resulting orbit might be:

Correct AnswerverifiedShow Answer

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

The rotational inertia of a uniform thin rod about its end is ML2/3, where M is the mass and L is the length. Such a rod is hung vertically from one end and set into small amplitude oscillation. If L = 1.0 m this rod will have the same period as a simple pendulum of length:

Correct AnswerverifiedShow Answer

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

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

Correct AnswerverifiedD

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

Correct AnswerverifiedShow Answer

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 AnswerverifiedShow Answer

Correct Answer
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Correct Answer
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Correct Answer
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Three physical pendulums, with masses m₁, m₂ = 2m₁, and m₃ = 3m₁, have the same shape and size and are suspended at the same point. Rank them according to their periods, from shortest to longest.

Correct Answer
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E

Correct Answer
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Correct Answer
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An object on the end of a spring is set into oscillation by giving it an initial velocity while it is at its equilibrium position. In the first trial the initial velocity is v₀ and in the second it is 4v₀. In the second trial:

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

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

Correct Answer
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Correct Answer
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D

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:

Correct Answer
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Correct Answer
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Correct Answer
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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:

Correct Answer
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The rotational inertia of a uniform thin rod about its end is ML²/3, where M is the mass and L is the length. Such a rod is hung vertically from one end and set into small amplitude oscillation. If L = 1.0 m this rod will have the same period as a simple pendulum of length:

Correct Answer
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Correct Answer
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Correct Answer
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D

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

Correct Answer
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Correct Answer
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