Question 1

A uniform disk (Icm =   MR2) of mass M and radius R is suspended from a point on its rim. If it oscillates as a physical pendulum its period is

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 2

Which of the following statements is true of a particle that is moving in simple harmonic motion?

Accepted Answer

A)  The momentum of the particle is constant. 
B)  The kinetic energy of the particle is constant. 
C)  The potential energy of Earth-particle system is constant. 
D)  The acceleration of the particle is constant. 
E)  The force the particle experiences is a negative restoring force. 
A)  The momentum of the particle is constant. 
B)  The kinetic energy of the particle is constant. 
C)  The potential energy of Earth-particle system is constant. 
D)  The acceleration of the particle is constant. 
E)  The force the particle experiences is a negative restoring force.

Question 3

A ball moves back and forth in simple harmonic motion along a line 12 cm long. When the ball is 4 cm from the left-hand end of its path, it has an acceleration of 24 cm/s2. When the ball is 1 cm from the right-hand end of its path the magnitude of its acceleration is

Accepted Answer

A)  15 cm/s2  
B)  30 cm/s2  
C)  3 cm/s2  
D)  60 cm/s2  
E)  88 cm/s2  
A)  15 cm/s2  
B)  30 cm/s2  
C)  3 cm/s2  
D)  60 cm/s2  
E)  88 cm/s2

Question 4

Use the figure to the right to answer the next problems.
A ball of mass m = 100 g and radius r = 10 cm is suspended from a light spring with spring constant k = 4 N/m. The ball is then immersed in oil with viscosity $\eta$ = 0.2 Pa.s and driven at the resonant frequency by a variable force F = FS1U1B1oS1U1B0 cos ($\omega$t) at an amplitude of A = 10 cm.  
-How much energy is dissipated per cycle?

Accepted Answer

A)  0.028 J 
B)  0.057 J 
C)  0.11 J 
D)  0.068 J 
E)  0.16 J 
A)  0.028 J 
B)  0.057 J 
C)  0.11 J 
D)  0.068 J 
E)  0.16 J

Question 5

The width of a resonance curve is an indication of

Accepted Answer

A)  the damping of the system. 
B)  the Q-value of the system. 
C)  the extent to which the system is oscillatory. 
D)  the rate at which energy is being dissipated each cycle. 
E)  all of the above 
A)  the damping of the system. 
B)  the Q-value of the system. 
C)  the extent to which the system is oscillatory. 
D)  the rate at which energy is being dissipated each cycle. 
E)  all of the above

Question 6

A mass on a spring oscillates with an amplitude of 5.0 cm. What is the position of the mass when the kinetic and potential energies are equal?

Accepted Answer

A)  There is not enough information provided to answer this question. 
B)  1.2 cm 
C)  2.5 cm 
D)  3.5 cm 
E)  3.8 cm 
A)  There is not enough information provided to answer this question. 
B)  1.2 cm 
C)  2.5 cm 
D)  3.5 cm 
E)  3.8 cm

Question 7

A particle moves in one dimension with simple harmonic motion according to the equation
D 2x/dt2 = - 4$\pi$2x
Where the units are SI. Its period is

Accepted Answer

A)  4$\pi$2 s 
B)  2$\pi$ s 
C)  1 s 
D)  1/(2$\pi$) s 
E)  1/(4$\pi$2) s 
A)  4$\pi$2 s 
B)  2$\pi$ s 
C)  1 s 
D)  1/(2$\pi$) s 
E)  1/(4$\pi$2) s

Question 8

A physical pendulum oscillates with small amplitude and a frequency of 2.00 Hz at a place where g is equal to 9.81 m/s2. The length of a simple pendulum that would oscillate with small amplitude at the same frequency is approximately

Accepted Answer

A)  6.10 cm 
B)  12.2 cm 
C)  97.5 cm 
D)  2.44 m 
E)  4.88 m 
A)  6.10 cm 
B)  12.2 cm 
C)  97.5 cm 
D)  2.44 m 
E)  4.88 m

Question 9

A body of mass 5.0 kg moves in simple harmonic motion according to the equation 
X = 0.040 sin(30t + $\pi$/6) 
Where the units are SI. The period of this motion is

Accepted Answer

A)  1/30 s 
B)  $\pi$/15 s 
C)  $\pi$/6 s 
D)  15/$\pi$ s 
E)  30 s 
A)  1/30 s 
B)  $\pi$/15 s 
C)  $\pi$/6 s 
D)  15/$\pi$ s 
E)  30 s

Question 10

The graph shows the period squared versus the length for a simple pendulum. The slope of the graph corresponds to

Accepted Answer

A)  1/g 
B)  g/(4$\pi$2) 
C)  g 
D)  4$\pi$2/g 
E)  4$\pi$2g 
A)  1/g 
B)  g/(4$\pi$2) 
C)  g 
D)  4$\pi$2/g 
E)  4$\pi$2g

Question 11

A particle is moving with SHM. If it has velocities of v1 and v2 when it is at positions x1 and x2 from the equilibrium position respectively, then the square of the frequency of vibration (f 2) is given by:

Accepted Answer

A)  (v12 - v22 ) / 4 $\pi$2 (x12 - x22 ) 
B)  (v12 - v22 ) / 4 $\pi$2 (x22 - x12 ) 
C)  (v12 + v22 ) / 4 $\pi$2 (x22 - x12 ) 
D)  (v12 + v22 ) / 2 $\pi$2 (x22 + x12 ) 
E)  (v12 + v22 ) / (x22 - x12 ) 
A)  (v12 - v22 ) / 4 $\pi$2 (x12 - x22 ) 
B)  (v12 - v22 ) / 4 $\pi$2 (x22 - x12 ) 
C)  (v12 + v22 ) / 4 $\pi$2 (x22 - x12 ) 
D)  (v12 + v22 ) / 2 $\pi$2 (x22 + x12 ) 
E)  (v12 + v22 ) / (x22 - x12 )

Question 12

A pendulum is oscillating with a total mechanical energy E0. When the pendulum is at its maximum displacement, the kinetic energy K and the potential energy U are

Accepted Answer

A)  K =   E0; U =   E0  
B)  K = 0; U = E0  
C)  K = E0; U = E0  
D)  K = E0; U = 0 
E)  K = E0; U =   E0  
A)  K =   E0; U =   E0  
B)  K = 0; U = E0  
C)  K = E0; U = E0  
D)  K = E0; U = 0 
E)  K = E0; U =   E0

Question 13

A long homogeneous rod can be pivoted as a physical pendulum at each of the points shown. Points at which the periods would be about the same are

Accepted Answer

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

Question 14

When driving over a washboard speed bumps, certain speeds make the bumps less "bumpy." Suppose your car has mass of 1000 kg and the critical damping constant of the shock absorbers is 12000 kg/s, what is the "ideal speed" to drive across the bumps assuming that the bumps are 0.3 m apart? Hint: Find the decay time for the critically damped shock absorbers.

Accepted Answer

A)  1.2 m/s 
B)  2.4 m/s 
C)  3.6 m/s 
D)  4.8 m/s 
E)  6 m/s 
A)  1.2 m/s 
B)  2.4 m/s 
C)  3.6 m/s 
D)  4.8 m/s 
E)  6 m/s

Question 15

When you push a child in a swing, you most likely

Accepted Answer

A)  push with as large a force as possible. 
B)  push with a periodic force as often as possible. 
C)  push with a periodic force, with a period that depends on the weight of the child. 
D)  push with a periodic force, with a period that depends on the length of the ropes on the swing. 
E)  push with a force equal to the weight of the child. 
A)  push with as large a force as possible. 
B)  push with a periodic force as often as possible. 
C)  push with a periodic force, with a period that depends on the weight of the child. 
D)  push with a periodic force, with a period that depends on the length of the ropes on the swing. 
E)  push with a force equal to the weight of the child.

Question 16

An object is moving with simple harmonic motion. When the object is displaced 4 cm from its equilibrium point, its acceleration is 20 cm/s2. Calculate the period T.

Accepted Answer

A)  0.45 s 
B)  0.36 s 
C)  2.2 s 
D)  2.8 s 
E)  none of the above 
A)  0.45 s 
B)  0.36 s 
C)  2.2 s 
D)  2.8 s 
E)  none of the above

Question 17

A damped oscillator has a decay time constant $\tau$. After time t = $\tau$ has passed, the fraction of the amount of energy remaining is

Accepted Answer

A)  0.25 
B)  0.37 
C)  0.5 
D)  0.67 
E)  0.75 
A)  0.25 
B)  0.37 
C)  0.5 
D)  0.67 
E)  0.75

Question 18

A particle moving in simple harmonic motion with a period T = 1.5 s passes through the equilibrium point at time t0 = 0 with a velocity of 1.00 m/s to the right. A time t later, the particle is observed to move to the left with a velocity of 0.50 m/s. (Note the change in direction of the velocity.) The smallest possible value of the time t is

Accepted Answer

A)  0.17 s 
B)  0.33 s 
C)  0.50 s 
D)  0.25 s 
E)  0.82 s 
A)  0.17 s 
B)  0.33 s 
C)  0.50 s 
D)  0.25 s 
E)  0.82 s

Question 19

Use the figure to answer the problem. A spring of negligible mass and spring constant k is attached to the wall on one end, and the other end is attached to the center of mass axis of a solid sphere of mass m and radius r. The spring is stretched a distance A from equilibrium and let go. The sphere rolls freely on a smooth surface.  
-The angular frequency of the oscillation is

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 20

A particle is moving with SHM. If it has velocities of 6 cm/s and 2 cm/s when it is at positions 4 cm and 7 cm respectively from the equilibrium position, then calculate its period of oscillation.

Accepted Answer

A)  5.4 s 
B)  6.4 s 
C)  7.4 s 
D)  10.8 s 
E)  none of the above 
A)  5.4 s 
B)  6.4 s 
C)  7.4 s 
D)  10.8 s 
E)  none of the above

A uniform disk (I_cm = MR²) of mass M and radius R is suspended from a point on its rim. If it oscillates as a physical pendulum its period is

Which of the following statements is true of a particle that is moving in simple harmonic motion?

A ball moves back and forth in simple harmonic motion along a line 12 cm long. When the ball is 4 cm from the left-hand end of its path, it has an acceleration of 24 cm/s². When the ball is 1 cm from the right-hand end of its path the magnitude of its acceleration is

The width of a resonance curve is an indication of

A mass on a spring oscillates with an amplitude of 5.0 cm. What is the position of the mass when the kinetic and potential energies are equal?

A particle moves in one dimension with simple harmonic motion according to the equation D ²x/dt² = - 4 $\pi$ ²x Where the units are SI. Its period is

A physical pendulum oscillates with small amplitude and a frequency of 2.00 Hz at a place where g is equal to 9.81 m/s². The length of a simple pendulum that would oscillate with small amplitude at the same frequency is approximately

A body of mass 5.0 kg moves in simple harmonic motion according to the equation X = 0.040 sin(30t + $\pi$ /6) Where the units are SI. The period of this motion is

The graph shows the period squared versus the length for a simple pendulum. The slope of the graph corresponds to

A particle is moving with SHM. If it has velocities of v₁ and v₂ when it is at positions x₁ and x₂ from the equilibrium position respectively, then the square of the frequency of vibration (f ²) is given by:

A pendulum is oscillating with a total mechanical energy E₀. When the pendulum is at its maximum displacement, the kinetic energy K and the potential energy U are

A long homogeneous rod can be pivoted as a physical pendulum at each of the points shown. Points at which the periods would be about the same are

When you push a child in a swing, you most likely

An object is moving with simple harmonic motion. When the object is displaced 4 cm from its equilibrium point, its acceleration is 20 cm/s². Calculate the period T.

A damped oscillator has a decay time constant $\tau$ . After time t = $\tau$ has passed, the fraction of the amount of energy remaining is

A particle is moving with SHM. If it has velocities of 6 cm/s and 2 cm/s when it is at positions 4 cm and 7 cm respectively from the equilibrium position, then calculate its period of oscillation.

Systems of Measurement

Motion in One Dimension

Motion in Two and Three Dimensions

Newtons Laws

Applications of Newtons Laws

Work and Energy

Conservation of Energy

Systems of Particles and Conservation of Linear Momentum

Rotation

Conservation of Angular Momentum

Gravity

Static Equilibrium and Elasticity

Fluids

Wave Motion

Superposition and Standing Waves

Temperature and the Kinetic Theory of Gases

Heat and the First Law of Thermodynamics

The Second Law of Thermodynamics

Thermal Properties and Processes

Filters

Exam 14: Oscillations

A uniform disk (Icm = MR2) of mass M and radius R is suspended from a point on its rim. If it oscillates as a physical pendulum its period is

Which of the following statements is true of a particle that is moving in simple harmonic motion?

A ball moves back and forth in simple harmonic motion along a line 12 cm long. When the ball is 4 cm from the left-hand end of its path, it has an acceleration of 24 cm/s2. When the ball is 1 cm from the right-hand end of its path the magnitude of its acceleration is

The width of a resonance curve is an indication of

A mass on a spring oscillates with an amplitude of 5.0 cm. What is the position of the mass when the kinetic and potential energies are equal?

A particle moves in one dimension with simple harmonic motion according to the equation D 2x/dt2 = - 4 π\piπ 2x Where the units are SI. Its period is

A physical pendulum oscillates with small amplitude and a frequency of 2.00 Hz at a place where g is equal to 9.81 m/s2. The length of a simple pendulum that would oscillate with small amplitude at the same frequency is approximately

A body of mass 5.0 kg moves in simple harmonic motion according to the equation X = 0.040 sin(30t + π\piπ /6) Where the units are SI. The period of this motion is

The graph shows the period squared versus the length for a simple pendulum. The slope of the graph corresponds to

A particle is moving with SHM. If it has velocities of v1 and v2 when it is at positions x1 and x2 from the equilibrium position respectively, then the square of the frequency of vibration (f 2) is given by:

A pendulum is oscillating with a total mechanical energy E0. When the pendulum is at its maximum displacement, the kinetic energy K and the potential energy U are

A long homogeneous rod can be pivoted as a physical pendulum at each of the points shown. Points at which the periods would be about the same are

When you push a child in a swing, you most likely

An object is moving with simple harmonic motion. When the object is displaced 4 cm from its equilibrium point, its acceleration is 20 cm/s2. Calculate the period T.

A damped oscillator has a decay time constant τ\tauτ . After time t = τ\tauτ has passed, the fraction of the amount of energy remaining is

A particle is moving with SHM. If it has velocities of 6 cm/s and 2 cm/s when it is at positions 4 cm and 7 cm respectively from the equilibrium position, then calculate its period of oscillation.

Systems of Measurement

Motion in One Dimension

Motion in Two and Three Dimensions

Newtons Laws

Applications of Newtons Laws

Work and Energy

Conservation of Energy

Systems of Particles and Conservation of Linear Momentum

Rotation

Conservation of Angular Momentum

Gravity

Static Equilibrium and Elasticity

Fluids

Wave Motion

Superposition and Standing Waves

Temperature and the Kinetic Theory of Gases

Heat and the First Law of Thermodynamics

The Second Law of Thermodynamics

Thermal Properties and Processes

Filters

A uniform disk (I_cm = MR²) of mass M and radius R is suspended from a point on its rim. If it oscillates as a physical pendulum its period is

A ball moves back and forth in simple harmonic motion along a line 12 cm long. When the ball is 4 cm from the left-hand end of its path, it has an acceleration of 24 cm/s². When the ball is 1 cm from the right-hand end of its path the magnitude of its acceleration is

A particle moves in one dimension with simple harmonic motion according to the equation D ²x/dt² = - 4 $\pi$ ²x Where the units are SI. Its period is

A physical pendulum oscillates with small amplitude and a frequency of 2.00 Hz at a place where g is equal to 9.81 m/s². The length of a simple pendulum that would oscillate with small amplitude at the same frequency is approximately

A body of mass 5.0 kg moves in simple harmonic motion according to the equation X = 0.040 sin(30t + $\pi$ /6) Where the units are SI. The period of this motion is

A particle is moving with SHM. If it has velocities of v₁ and v₂ when it is at positions x₁ and x₂ from the equilibrium position respectively, then the square of the frequency of vibration (f ²) is given by:

A pendulum is oscillating with a total mechanical energy E₀. When the pendulum is at its maximum displacement, the kinetic energy K and the potential energy U are

An object is moving with simple harmonic motion. When the object is displaced 4 cm from its equilibrium point, its acceleration is 20 cm/s². Calculate the period T.

A damped oscillator has a decay time constant $\tau$ . After time t = $\tau$ has passed, the fraction of the amount of energy remaining is