Question 1

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 maximum speed of the block is:

Accepted Answer

A)  0.06 m/s 
B)  0.17 m/s 
C)  0.24 m/s 
D)  4.9 m/s 
E)  6.9 m/s 
A)  0.06 m/s 
B)  0.17 m/s 
C)  0.24 m/s 
D)  4.9 m/s 
E)  6.9 m/s

Question 2

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 3

A simple pendulum has length L and period T. As it passes through its equilibrium position, the string is suddenly clamped at its mid-point. The period then becomes:

Accepted Answer

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

Question 4

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 5

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 6

A simple pendulum consists of a small ball tied to a string and set in oscillation. As the pendulum swings the tension in the string is:

Accepted Answer

A)  constant 
B)  a sinusoidal function of time 
C)  the square of a sinusoidal function of time 
D)  the reciprocal of a sinusoidal function of time 
E)  none of the above 
A)  constant 
B)  a sinusoidal function of time 
C)  the square of a sinusoidal function of time 
D)  the reciprocal of a sinusoidal function of time 
E)  none of the above

Question 7

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 8

The period of a simple pendulum is 1 s on Earth. When brought to a planet where g is one-tenth that on Earth, its period becomes:

Accepted Answer

A)  1 s 
B)    
C)  1/10 s 
D)    
E)  10 s 
A)  1 s 
B)    
C)  1/10 s 
D)    
E)  10 s

Question 9

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 10

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 it is at x = -1/2 xm, its total energy is:

Accepted Answer

A)  0 J 
B)  3 J 
C)  4 J 
D)  5 J 
E)  8 J 
A)  0 J 
B)  3 J 
C)  4 J 
D)  5 J 
E)  8 J

Question 11

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 12

A block on a spring is subjected to an applied sinusoidal force AND to a damping force that is proportional to its velocity. The energy dissipated by damping is supplied by:

Accepted Answer

A)  the potential energy of the spring 
B)  the kinetic energy of the mass 
C)  gravity 
D)  friction 
E)  the applied force 
A)  the potential energy of the spring 
B)  the kinetic energy of the mass 
C)  gravity 
D)  friction 
E)  the applied force

Question 13

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 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

In simple harmonic motion, the magnitude of the acceleration is:

Accepted Answer

A)  constant 
B)  proportional to the displacement 
C)  inversely proportional to the displacement 
D)  greatest when the velocity is greatest 
E)  never greater than g 
A)  constant 
B)  proportional to the displacement 
C)  inversely proportional to the displacement 
D)  greatest when the velocity is greatest 
E)  never greater than g

Question 16

Which of the following is NOT required for a simple pendulum undergoing simple harmonic oscillation?

Accepted Answer

A)  a point mass 
B)  a massless string 
C)  a small amplitude 
D)  gravitational force 
E)  a large spring constant 
A)  a point mass 
B)  a massless string 
C)  a small amplitude 
D)  gravitational force 
E)  a large spring constant

Question 17

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 
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

Question 18

In simple harmonic motion, the magnitude of the acceleration is greatest when:

Accepted Answer

A)  the displacement is zero 
B)  the displacement is maximum 
C)  the speed is maximum 
D)  the force is zero 
E)  the speed is between zero and its maximum 
A)  the displacement is zero 
B)  the displacement is maximum 
C)  the speed is maximum 
D)  the force is zero 
E)  the speed is between zero and its maximum

Question 19

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 20

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

Exam 15: Oscillations

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 maximum speed of the block is:

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 simple pendulum has length L and period T. As it passes through its equilibrium position, the string is suddenly clamped at its mid-point. The period then becomes:

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.

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

A simple pendulum consists of a small ball tied to a string and set in oscillation. As the pendulum swings the tension in the string is:

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:

The period of a simple pendulum is 1 s on Earth. When brought to a planet where g is one-tenth that on Earth, its period becomes:

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:

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 it is at x = -1/2 xm, its total energy is:

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 block on a spring is subjected to an applied sinusoidal force AND to a damping force that is proportional to its velocity. The energy dissipated by damping is supplied by:

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?

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

In simple harmonic motion, the magnitude of the acceleration is:

Which of the following is NOT required for a simple pendulum undergoing simple harmonic oscillation?

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

In simple harmonic motion, the magnitude of the acceleration is greatest when:

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:

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:

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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.

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:

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 it is at x = -1/2 x_m, its total energy is:

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 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: