Question 1

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 torque 
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 torque

Question 2

A block attached to a spring undergoes simple harmonic motion on a horizontal frictionless surface.Its total energy is 50 J.When the displacement is half the amplitude, the kinetic energy is:

Accepted Answer

A) 0 J 
B) 12.5 J 
C) 25 J 
D) 37.5 J 
E) 50 J 
A) 0 J 
B) 12.5 J 
C) 25 J 
D) 37.5 J 
E) 50 J

Question 3

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

Accepted Answer

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

Question 4

A disk whose rotational inertia is 450 kg∙m2 hangs from a wire whose torsion constant is 2300 N∙m/rad.When its angular displacement is −0.23 rad, what is its angular acceleration?

Accepted Answer

A) 1.0 x 10-2 rad/s2 
B) 4.5 x 10-2 rad/s2 
C) 0.23 rad/s2 
D) 0.52 rad/s2 
E) 1.2 rad/s2 
A) 1.0 x 10-2 rad/s2 
B) 4.5 x 10-2 rad/s2 
C) 0.23 rad/s2 
D) 0.52 rad/s2 
E) 1.2 rad/s2

Question 5

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

Question 6

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

Accepted Answer

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   is the same 
E) they are started so the combination   is the same 
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   is the same 
E) they are started so the combination   is the same

Question 7

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

Accepted Answer

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

Question 8

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

Question 9

A mass-spring system is oscillating with amplitude A.The kinetic energy will equal the potential energy only when the displacement is

Accepted Answer

A) "0" 
B) "   A/4" 
C)  " " 
D) "   A/2" 
E) "anywhere between -A and +A" 
A) "0" 
B) "   A/4" 
C)  " " 
D) "   A/2" 
E) "anywhere between -A and +A"

Question 10

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

Accepted Answer

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

Question 11

A particle is in simple harmonic motion along the x axis.The amplitude of the motion is xm.When it is at x = x1, its kinetic energy is K = 5 J and its potential energy (measured with U = 0 at x = 0)is U = 3 J.When its kinetic energy is 8 J, it is at:

Accepted Answer

A) x = 0 
B) x = x1 
C) x = xm/2 
D) x = xm/   
E) x = xm 
A) x = 0 
B) x = x1 
C) x = xm/2 
D) x = xm/   
E) x = xm

Question 12

A particle is in simple harmonic motion along the x axis.The amplitude of the motion is xm.At one point in its motion its kinetic energy is K = 5 J and its potential energy (measured with U = 0 at x = 0)is U = 3 J.When it is at x = xm, the kinetic and potential energies are:

Accepted Answer

A) K = 5 J and U = 3 J 
B) K = 5 J and U = -3 J 
C) K = 8 J and U = 0 J 
D) K = 0 J and U = 8 J 
E) K = 0 J and U = -8 J 
A) K = 5 J and U = 3 J 
B) K = 5 J and U = -3 J 
C) K = 8 J and U = 0 J 
D) K = 0 J and U = 8 J 
E) K = 0 J and U = -8 J

Question 13

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

Accepted Answer

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

Question 14

If the length of a simple pendulum is doubled, its period will:

Accepted Answer

A) halve 
B) increase by a factor of   
C) decrease by a factor of   
D) double 
E) remain the same 
A) halve 
B) increase by a factor of   
C) decrease by a factor of   
D) double 
E) remain the same

Question 15

Five hoops are each pivoted at a point on the rim and allowed to swing as physical pendulums.The masses and radii are   Order the hoops according to the periods of their motions, smallest to largest.

Accepted Answer

A) 1, 2, 3, 4, 5 
B) 5, 4, 3, 2, 1 
C) 1, 2, 3, 5, 4 
D) 1, 2, 5, 4, 3 
E) 5, 4, 1, 2, 3 
A) 1, 2, 3, 4, 5 
B) 5, 4, 3, 2, 1 
C) 1, 2, 3, 5, 4 
D) 1, 2, 5, 4, 3 
E) 5, 4, 1, 2, 3

Question 16

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

Question 17

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 square 
A) an ellipse 
B) a circle 
C) a parabola 
D) a hyperbola 
E) a square

Question 18

A meter stick is pivoted at a point a distance a from its center and swings as a physical pendulum.Of the following values for a, which results in the shortest period of oscillation?

Accepted Answer

A) a = 0.1 m 
B) a = 0.2 m 
C) a = 0.3 m 
D) a = 0.4 m 
E) a = 0.5 m 
A) a = 0.1 m 
B) a = 0.2 m 
C) a = 0.3 m 
D) a = 0.4 m 
E) a = 0.5 m

Question 19

Let U be the potential energy (with the zero at zero displacement)and K be the kinetic energy of a simple harmonic oscillator.Uavg and Kavg are the average values over a cycle.Then:

Accepted Answer

A) Kavg > Uavg 
B) Kavg avg 
C) Kavg = Uavg 
D) K = 0 when U = 0 
E) K + U = 0 
A) Kavg > Uavg 
B) Kavg avg 
C) Kavg = Uavg 
D) K = 0 when U = 0 
E) K + U = 0

Question 20

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 great 
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 great

Exam 15: Oscillations

An angular simple harmonic oscillator:

A block attached to a spring undergoes simple harmonic motion on a horizontal frictionless surface.Its total energy is 50 J.When the displacement is half the amplitude, the kinetic energy is:

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

A disk whose rotational inertia is 450 kg∙m2 hangs from a wire whose torsion constant is 2300 N∙m/rad.When its angular displacement is −0.23 rad, what is its angular acceleration?

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:

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

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

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

A mass-spring system is oscillating with amplitude A.The kinetic energy will equal the potential energy only when the displacement is

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

A particle is in simple harmonic motion along the x axis.The amplitude of the motion is xm.When it is at x = x1, its kinetic energy is K = 5 J and its potential energy (measured with U = 0 at x = 0)is U = 3 J.When its kinetic energy is 8 J, it is at:

A particle is in simple harmonic motion along the x axis.The amplitude of the motion is xm.At one point in its motion its kinetic energy is K = 5 J and its potential energy (measured with U = 0 at x = 0)is U = 3 J.When it is at x = xm, the kinetic and potential energies are:

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

If the length of a simple pendulum is doubled, its period will:

Five hoops are each pivoted at a point on the rim and allowed to swing as physical pendulums.The masses and radii are Order the hoops according to the periods of their motions, smallest to largest.

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:

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:

A meter stick is pivoted at a point a distance a from its center and swings as a physical pendulum.Of the following values for a, which results in the shortest period of oscillation?

Let U be the potential energy (with the zero at zero displacement)and K be the kinetic energy of a simple harmonic oscillator.Uavg and Kavg are the average values over a cycle.Then:

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:

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A disk whose rotational inertia is 450 kg∙m² hangs from a wire whose torsion constant is 2300 N∙m/rad.When its angular displacement is −0.23 rad, what is its angular acceleration?

A particle is in simple harmonic motion along the x axis.The amplitude of the motion is x_m.When it is at x = x₁, its kinetic energy is K = 5 J and its potential energy (measured with U = 0 at x = 0)is U = 3 J.When its kinetic energy is 8 J, it is at:

A particle is in simple harmonic motion along the x axis.The amplitude of the motion is x_m.At one point in its motion its kinetic energy is K = 5 J and its potential energy (measured with U = 0 at x = 0)is U = 3 J.When it is at x = x_m, the kinetic and potential energies are:

Let U be the potential energy (with the zero at zero displacement)and K be the kinetic energy of a simple harmonic oscillator.U_avg and K_avg are the average values over a cycle.Then:

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: