Question 1

A weight suspended from an ideal spring oscillates up and down with a period T. If the amplitude of the oscillation is doubled, the period will be:

Accepted Answer

A)  T 
B)  1.5 T 
C)  2T 
D)  T/2 
E)  4T 
A)  T 
B)  1.5 T 
C)  2T 
D)  T/2 
E)  4T

Question 2

A simple pendulum of length L and mass M has frequency f. To increase its frequency to 2f:

Accepted Answer

A)  increase its length to 4L 
B)  increase its length to 2L 
C)  decrease its length to L/2 
D)  decrease its length to L/4 
E)  decrease its mass to < M/4 
A)  increase its length to 4L 
B)  increase its length to 2L 
C)  decrease its length to L/2 
D)  decrease its length to L/4 
E)  decrease its mass to < M/4

Question 3

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 4

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 5

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

Question 6

A particle is in simple harmonic motion with period T. At time t = 0 it is at the equilibrium point. At the times listed below it is at various points in its cycle. Which of them is farthest away from the equilibrium point?

Accepted Answer

A)  0.5T 
B)  0.7T 
C)  T 
D)  1.4T 
E)  1.5T 
A)  0.5T 
B)  0.7T 
C)  T 
D)  1.4T 
E)  1.5T

Question 7

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 8

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

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 given 
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 given

Question 9

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

Question 10

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 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 there 
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 there

Question 12

The displacement of an object oscillating on a spring is given by x(t) = xmcos(  $ \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:

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 ($\phi$  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 ($\phi$  is exactly 0,  $\pi$/2,  $\pi$, or 3 $\pi$/2 radians)

Question 13

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

Question 14

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 15

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

Exam 15: Oscillations

A weight suspended from an ideal spring oscillates up and down with a period T. If the amplitude of the oscillation is doubled, the period will be:

A simple pendulum of length L and mass M has frequency f. To increase its frequency to 2f:

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?

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

A particle is in simple harmonic motion with period T. At time t = 0 it is at the equilibrium point. At the times listed below it is at various points in its cycle. Which of them is farthest away from the equilibrium point?

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:

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

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

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:

A particle oscillating in simple harmonic motion is:

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:

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

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 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?

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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?

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:

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:

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?