Question 1

A 1.2-kg mass is oscillating without friction on a spring whose spring constant is 3400 N/m.When the mass's displacement is 7.2 cm, what is its acceleration?

Accepted Answer

A) −3.8 m/s2 
B) −200 m/s2 
C) −240 m/s2 
D) −2.0 x 104 m/s2 
E) cannot be calculated without more information 
A) −3.8 m/s2 
B) −200 m/s2 
C) −240 m/s2 
D) −2.0 x 104 m/s2 
E) cannot be calculated without more information

Question 2

Which of the following is the difference between a simple pendulum and a physical pendulum?

Accepted Answer

A) The physical pendulum does not rotate around its center of mass. 
B) The physical pendulum does not depend on the acceleration of gravity. 
C) The physical pendulum has an extended mass. 
D) The simple pendulum has a small amplitude. 
E) The physical pendulum rotates around its center of mass. 
A) The physical pendulum does not rotate around its center of mass. 
B) The physical pendulum does not depend on the acceleration of gravity. 
C) The physical pendulum has an extended mass. 
D) The simple pendulum has a small amplitude. 
E) The physical pendulum rotates around its center of mass.

Question 3

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 maximum speed of the block is:

Accepted Answer

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

Question 4

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

Accepted Answer

A) "0 and  $\pi$ /2 radians" 
B) "  $\pi$ /2 and   $\pi$  radians" 
C) " $\pi$ and 3 $\pi$/2 radians" 
D) "3  $\pi$ /2 and 2  $\pi$  radians" 
E) "none of the above (    is exactly 0,   $\pi$ /2,   $\pi$ , or 3  $\pi$ /2 radians)" 
A) "0 and  $\pi$ /2 radians" 
B) "  $\pi$ /2 and   $\pi$  radians" 
C) " $\pi$ and 3 $\pi$/2 radians" 
D) "3  $\pi$ /2 and 2  $\pi$  radians" 
E) "none of the above (    is exactly 0,   $\pi$ /2,   $\pi$ , or 3  $\pi$ /2 radians)"

Question 5

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 three are the same 
A) 1, 2, 3 
B) 3, 2, 1 
C) 2, 3, 1 
D) 2, 1, 3 
E) All three are the same

Question 6

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

Question 7

An oscillatory motion must be simple harmonic if:

Accepted Answer

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 
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

Question 8

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

Question 9

A 3-kg block, attached to a spring, executes simple harmonic motion according to x = 2cos(50t)where x is in meters and t is in seconds.The spring constant of the spring is:

Accepted Answer

A) 1 N/m 
B) 100 N/m 
C) 150 N/m 
D) 7500 N/m 
E) none of these 
A) 1 N/m 
B) 100 N/m 
C) 150 N/m 
D) 7500 N/m 
E) none of these

Question 10

At the instant its angular displacement is 0.32 rad, the angular acceleration of a physical pendulum is -630 rad/s2.What is its angular frequency of oscillation?

Accepted Answer

A) 6.6 rad/s 
B) 14 rad/s 
C) 20 rad/s 
D) 44 rad/s 
E) 200 rad/s 
A) 6.6 rad/s 
B) 14 rad/s 
C) 20 rad/s 
D) 44 rad/s 
E) 200 rad/s

Question 11

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 desired 
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 desired

Question 12

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

Question 13

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

Question 14

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 potential 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 15

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 = -xm 
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 = -xm

Question 16

Two uniform spheres are pivoted on horizontal axes that are tangent to their surfaces.The one with the longer period of oscillation is the one with:

Accepted Answer

A) the larger mass 
B) the smaller mass 
C) the larger rotational inertia 
D) the smaller rotational inertia 
E) the larger radius 
A) the larger mass 
B) the smaller mass 
C) the larger rotational inertia 
D) the smaller rotational inertia 
E) the larger radius

Question 17

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 particle's position at t = 5.0 s?

Accepted Answer

A) -1.5 m 
B) -0.73 m 
C) 0 m 
D) 0.73 m 
E) 1.5 m 
A) -1.5 m 
B) -0.73 m 
C) 0 m 
D) 0.73 m 
E) 1.5 m

Question 18

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

Accepted Answer

A) "0 radians" 
B) "$\pi$/2 radians" 
C) "$\pi$ radians" 
D) "3$\pi$/2 radians" 
E) "2$\pi$ radians" 
A) "0 radians" 
B) "$\pi$/2 radians" 
C) "$\pi$ radians" 
D) "3$\pi$/2 radians" 
E) "2$\pi$ radians"

Question 19

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 speed 
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 speed

Question 20

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 above 
A) the damping force 
B) the initial amplitude 
C) the initial velocity 
D) the force of gravity 
E) none of the above

Exam 15: Oscillations

A 1.2-kg mass is oscillating without friction on a spring whose spring constant is 3400 N/m.When the mass's displacement is 7.2 cm, what is its acceleration?

Which of the following is the difference between a simple pendulum and a physical pendulum?

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 maximum speed of the block is:

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

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.

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:

An oscillatory motion must be simple harmonic if:

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:

A 3-kg block, attached to a spring, executes simple harmonic motion according to x = 2cos(50t)where x is in meters and t is in seconds.The spring constant of the spring is:

At the instant its angular displacement is 0.32 rad, the angular acceleration of a physical pendulum is -630 rad/s2.What is its angular frequency of oscillation?

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:

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:

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?

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 potential energy is 8 J, it is at:

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:

Two uniform spheres are pivoted on horizontal axes that are tangent to their surfaces.The one with the longer period of oscillation is the one with:

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 particle's position at t = 5.0 s?

The displacement of an object oscillating on a spring is given by x(t)= xmcos(+ ).If the initial displacement is zero and the initial velocity is in the negative x direction, then the phase constant 11ef007a_3990_6877_bc85_811eff4e9b0d_TB6585_11 is:

The amplitude of any oscillator will be doubled by:

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

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.

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:

At the instant its angular displacement is 0.32 rad, the angular acceleration of a physical pendulum is -630 rad/s².What is its angular frequency of oscillation?

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?

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 potential energy is 8 J, it is at:

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:

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 particle's position at t = 5.0 s?

The displacement of an object oscillating on a spring is given by x(t)= x_mcos(+ ).If the initial displacement is zero and the initial velocity is in the negative x direction, then the phase constant 11ef007a_3990_6877_bc85_811eff4e9b0d_TB6585_11 is: