Question 1

If the length of a simple pendulum is increased by 4% and the mass is decreased by 4%,the period is

Accepted Answer

A) not changed. 
B) increased by 2%. 
C) decreased by 4%. 
D) increased by 4%. 
E) decreased by 2%. 
A) not changed. 
B) increased by 2%. 
C) decreased by 4%. 
D) increased by 4%. 
E) decreased by 2%. B

Question 2

When the compression of a spring is doubled,the potential energy stored in the spring is

Accepted Answer

A) the same as before. 
B) doubled. 
C) tripled. 
D) increased by a factor of 8. 
E) None of these is correct. 
A) the same as before. 
B) doubled. 
C) tripled. 
D) increased by a factor of 8. 
E) None of these is correct. E

Question 3

The force constant for a simple harmonic motion is k and the amplitude of the motion is A.The maximum value of the potential energy of a mass m oscillating with simple harmonic motion is

Accepted Answer

A)    
B)    kA2  
C) kA2  
D) kA 
E) None of these is correct. 
A)    
B)    kA2  
C) kA2  
D) kA 
E) None of these is correct. B

Question 4

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 5

Use the following to answer question:  
-The graph shows the displacement of an oscillator as a function of time.The oscillator that is overdamped is

Accepted Answer

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

Question 6

A particle moving in a circle of radius 15 cm makes 33.3 rev/min.If the particle starts on the positive x axis at time t = 0,what is the x component of the particle's velocity at time t = 1.2 s?

Accepted Answer

A) 45 cm/s 
B) -3.8 cm/s 
C) 26 cm/s 
D) -45 cm/s 
E) 13 cm/s 
A) 45 cm/s 
B) -3.8 cm/s 
C) 26 cm/s 
D) -45 cm/s 
E) 13 cm/s

Question 7

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 8

Use the following to answer question:  
-The graph shows the displacement of an oscillator as a function of time.The oscillator that is critically damped is

Accepted Answer

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

Question 9

The kinetic energy K of a body executing simple harmonic motion is plotted against time,the time being expressed in terms of the period T.The initial conditions are such that the phase angle is zero.Such a graph would most closely resemble which of the following graphs?

Accepted Answer

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

Question 10

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 11

Use the following to answer question:  
-The graph shows the average power delivered to an oscillating system as a function of the driving frequency.According to these data,the damping is greatest for system(s)

Accepted Answer

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

Question 12

The acceleration of a particle moving with simple harmonic motion is given by   where x is in meters and a is in meters per second squared.The period of the motion is

Accepted Answer

A) 0.25 s 
B) 0.392 s 
C) 1.57 s 
D) 4.0 s 
E) 25.2 s 
A) 0.25 s 
B) 0.392 s 
C) 1.57 s 
D) 4.0 s 
E) 25.2 s

Question 13

What is the length L of a simple pendulum with the same period as a physical pendulum consisting of a hoop suspended at its rim?

Accepted Answer

A) L =   R 
B) L = 1/R 
C)    
D) L = R 
E) L = 2R 
A) L =   R 
B) L = 1/R 
C)    
D) L = R 
E) L = 2R

Question 14

The period of oscillation of a simple pendulum of length 9.8 m and mass 5.0 kg is approximately

Accepted Answer

A) 0.10 s 
B) 0.16 s 
C) 2.0 s 
D) 5.0 s 
E) 6.3 s 
A) 0.10 s 
B) 0.16 s 
C) 2.0 s 
D) 5.0 s 
E) 6.3 s

Question 15

A 1.81-kg block slides on a horizontal frictionless table with a speed of 1.22 m/s.It is brought to rest by compressing a spring in its path.If the spring has a force constant of 7.30 N/m,it is compressed

Accepted Answer

A) 6.89 m 
B) 1.22 m 
C) 1.71 m 
D) 0.305 m 
E) by none of these amounts 
A) 6.89 m 
B) 1.22 m 
C) 1.71 m 
D) 0.305 m 
E) by none of these amounts

Question 16

A body of mass 0.50 kg moves in simple harmonic motion with a period of 1.5 s and an amplitude of 20 mm.Which of the following equations correctly represents this motion?

Accepted Answer

A) x = 40 cos(t/1.5)mm 
B) x = 40 cos(2$\pi$t/1.5)mm 
C) x = 20 sin(t/1.5)mm 
D) x = 20 sin(1.5$\pi$t)mm 
E) x = 20 sin(2$\pi$t/1.5)mm 
A) x = 40 cos(t/1.5)mm 
B) x = 40 cos(2$\pi$t/1.5)mm 
C) x = 20 sin(t/1.5)mm 
D) x = 20 sin(1.5$\pi$t)mm 
E) x = 20 sin(2$\pi$t/1.5)mm

Question 17

Which of the following statements concerning the motion of a simple pendulum is incorrect?

Accepted Answer

A) The kinetic energy is a maximum when the displacement is a maximum. 
B) The acceleration is a maximum when the displacement is a maximum. 
C) The period is changed if the mass of the bob is doubled and the length of the pendulum is halved. 
D) The time interval between conditions of maximum potential energy is one period. 
E) The velocity is a maximum when the acceleration is a minimum. 
A) The kinetic energy is a maximum when the displacement is a maximum. 
B) The acceleration is a maximum when the displacement is a maximum. 
C) The period is changed if the mass of the bob is doubled and the length of the pendulum is halved. 
D) The time interval between conditions of maximum potential energy is one period. 
E) The velocity is a maximum when the acceleration is a minimum.

Question 18

A pendulum does not have simple harmonic motion if its angular amplitude $\theta$0 is not small.For large angular amplitudes,the period is given by T = T0[1 + (1/4)sin2 $\theta$0 + (3/64)sin4 $\theta$0 + · · · ]
As the angular amplitude of the pendulum gets larger,the frequency of the pendulum

Accepted Answer

A) does not change. 
B) increases. 
C) decreases. 
D) does whatever the period does. 
E) changes in proportion to T0. 
A) does not change. 
B) increases. 
C) decreases. 
D) does whatever the period does. 
E) changes in proportion to T0.

Question 19

A spring vibrates in simple harmonic motion according to the equation   where x is in centimeters and t is in seconds.The total number of vibrations this body makes in 10 s is

Accepted Answer

A) 0.5 
B) 10 
C) $\pi$ 
D) 15 
E) 5 
A) 0.5 
B) 10 
C) $\pi$ 
D) 15 
E) 5

Question 20

A thin test tube is partially filled with lead pellets so that it floats vertically in a fluid.Use Archimedes' Principle to calculate that if displaced slightly from its equilibrium position the test tube will undergo SHM in the vertical direction and derive how the time period is related to the density of the fluid.

Accepted Answer

A) T proportional to $\rho$(liquid) 
B) T proportional to $\rho$(liquid)1/2  
C) T proportional to $\rho$(liquid)2  
D) T proportional to $\rho$(liquid)-2  
E) T proportional to $\rho$(liquid)-1/2  
A) T proportional to $\rho$(liquid) 
B) T proportional to $\rho$(liquid)1/2  
C) T proportional to $\rho$(liquid)2  
D) T proportional to $\rho$(liquid)-2  
E) T proportional to $\rho$(liquid)-1/2

Exam 14: Oscillations

If the length of a simple pendulum is increased by 4% and the mass is decreased by 4%,the period is

When the compression of a spring is doubled,the potential energy stored in the spring is

The force constant for a simple harmonic motion is k and the amplitude of the motion is A.The maximum value of the potential energy of a mass m oscillating with simple harmonic motion is

The width of a resonance curve is an indication of

Use the following to answer question: -The graph shows the displacement of an oscillator as a function of time.The oscillator that is overdamped is

A particle moving in a circle of radius 15 cm makes 33.3 rev/min.If the particle starts on the positive x axis at time t = 0,what is the x component of the particle's velocity at time t = 1.2 s?

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

Use the following to answer question: -The graph shows the displacement of an oscillator as a function of time.The oscillator that is critically damped is

The kinetic energy K of a body executing simple harmonic motion is plotted against time,the time being expressed in terms of the period T.The initial conditions are such that the phase angle is zero.Such a graph would most closely resemble which of the following graphs?

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

Use the following to answer question: -The graph shows the average power delivered to an oscillating system as a function of the driving frequency.According to these data,the damping is greatest for system(s)

The acceleration of a particle moving with simple harmonic motion is given by where x is in meters and a is in meters per second squared.The period of the motion is

What is the length L of a simple pendulum with the same period as a physical pendulum consisting of a hoop suspended at its rim?

The period of oscillation of a simple pendulum of length 9.8 m and mass 5.0 kg is approximately

A 1.81-kg block slides on a horizontal frictionless table with a speed of 1.22 m/s.It is brought to rest by compressing a spring in its path.If the spring has a force constant of 7.30 N/m,it is compressed

A body of mass 0.50 kg moves in simple harmonic motion with a period of 1.5 s and an amplitude of 20 mm.Which of the following equations correctly represents this motion?

Which of the following statements concerning the motion of a simple pendulum is incorrect?

A spring vibrates in simple harmonic motion according to the equation where x is in centimeters and t is in seconds.The total number of vibrations this body makes in 10 s is

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