Question 1

An oscillator has a quality factor of 300.By what percentage does its energy decrease in each cycle?

Accepted Answer

A) 0.33% 
B) 1% 
C) 2% 
D) 3% 
E) 4% 
A) 0.33% 
B) 1% 
C) 2% 
D) 3% 
E) 4%

Question 2

In simple harmonic motion,the displacement x = A cos $\omega$t and the acceleration a = -$\omega$2x.If A = 0.25 m and the period is 0.32 s,the acceleration when t = 0.12 s is

Accepted Answer

A) zero 
B) +3.9 m/s2  
C) -3.9 m/s2  
D) +6.8 m/s2  
E) -6.8 m/s2  
A) zero 
B) +3.9 m/s2  
C) -3.9 m/s2  
D) +6.8 m/s2  
E) -6.8 m/s2

Question 3

If F is the force,x the displacement,and k a particular constant,for simple harmonic motion we must have

Accepted Answer

A) F = -k/x2  
B) F = k/x 
C) F = (k/x2)1/2  
D) F = -kx2  
E) None of these is correct. 
A) F = -k/x2  
B) F = k/x 
C) F = (k/x2)1/2  
D) F = -kx2  
E) None of these is correct.

Question 4

Use the figure to the right to answer the next two 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 F1F1F1S1= 0.2 PaF1F1F1S1.s and driven at the resonant frequency by a variable force F = FS1U1B10S1U1B0 cos (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

An oscillator has a quality factor of 100.By what percentage does its energy decrease in each cycle?

Accepted Answer

A) 2% 
B) 3% 
C) 4% 
D) 5% 
E) 6% 
A) 2% 
B) 3% 
C) 4% 
D) 5% 
E) 6%

Question 6

Use the figure to the right to answer the next two 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 F1F1F1S1= 0.2 PaF1F1F1S1.s and driven at the resonant frequency by a variable force F = FS1U1B10S1U1B0 cos (t) at an amplitude of A = 10 cm.
-What is the value of Fo?

Accepted Answer

A) 0.12 N 
B) 0.24 N 
C) 0.056 N 
D) 1.8 N 
E) 0.67 N 
A) 0.12 N 
B) 0.24 N 
C) 0.056 N 
D) 1.8 N 
E) 0.67 N

Question 7

The displacement in simple harmonic motion is a maximum when the

Accepted Answer

A) acceleration is zero. 
B) velocity is a maximum. 
C) velocity is zero. 
D) kinetic energy is a maximum. 
E) potential energy is a minimum. 
A) acceleration is zero. 
B) velocity is a maximum. 
C) velocity is zero. 
D) kinetic energy is a maximum. 
E) potential energy is a minimum.

Question 8

A 2.5-kg object is attached to a spring of force constant k = 4.5 kN/m.The spring is stretched 10 cm from equilibrium and released.What is the kinetic energy of the mass-spring system when the mass is 5.0 cm from its equilibrium position?

Accepted Answer

A) 5.6 J 
B) 11 J 
C) 17 J 
D) 14 J 
E) 42 J 
A) 5.6 J 
B) 11 J 
C) 17 J 
D) 14 J 
E) 42 J

Question 9

Use the figure to answer the next 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.  
-What is the linear kinetic energy when the sphere is at the equilibrium position?

Accepted Answer

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

Question 10

You want a mass that,when hung on the end of a spring,oscillates with a period of 1 s.If the spring has a spring constant of 10 N/m,the mass should be

Accepted Answer

A) 10 kg 
B)    kg 
C) 4$\pi$2(10)kg 
D) 10/(4$\pi$2)kg 
E) None of these is correct. 
A) 10 kg 
B)    kg 
C) 4$\pi$2(10)kg 
D) 10/(4$\pi$2)kg 
E) None of these is correct.

Question 11

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 12

A 10-kg block starts from rest at a vertical height of 1 m on a 30º frictionless inclined plane.If the block slides down the incline and then 20 m along a frictionless horizontal surface into a fixed spring with a force constant of 100 N/m,the spring is compressed approximately

Accepted Answer

A) 1.4 m 
B) 2.0 m 
C) 0.33 m 
D) 0.98 m 
E) 2.5 m 
A) 1.4 m 
B) 2.0 m 
C) 0.33 m 
D) 0.98 m 
E) 2.5 m

Question 13

A body of mass M is executing simple harmonic motion with an amplitude of 8.0 cm and a maximum acceleration of 100 cm/s2.When the displacement of this body from the equilibrium position is 6.0 cm,the magnitude of the acceleration is approximately

Accepted Answer

A) 8.7 cm/s2  
B) 21 cm/s2  
C) 35 cm/s2  
D) 17 cm/s2  
E) 1.3 m/s2  
A) 8.7 cm/s2  
B) 21 cm/s2  
C) 35 cm/s2  
D) 17 cm/s2  
E) 1.3 m/s2

Question 14

For a simple pendulum to have a period of 1 s it must have a length of

Accepted Answer

A) 1.0 m 
B) 0.25 m 
C) 9.8 m 
D) 4.0 m 
E) 2.7 m 
A) 1.0 m 
B) 0.25 m 
C) 9.8 m 
D) 4.0 m 
E) 2.7 m

Question 15

What is the amplitude after 1 s?

Accepted Answer

A) 2 cm 
B) 0.63 cm 
C) 0.96 cm 
D) 0.30 cm 
E) 0.15 cm 
A) 2 cm 
B) 0.63 cm 
C) 0.96 cm 
D) 0.30 cm 
E) 0.15 cm

Question 16

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

Accepted Answer

A) the resonant frequency is greater than $\omega$o. 
B) the system corresponding to curve 1 has the smallest quality factor. 
C) the system corresponding to curve 4 has the smallest quality factor. 
D) the resonant frequency is less than $\omega$o. 
E) None of these is correct. 
A) the resonant frequency is greater than $\omega$o. 
B) the system corresponding to curve 1 has the smallest quality factor. 
C) the system corresponding to curve 4 has the smallest quality factor. 
D) the resonant frequency is less than $\omega$o. 
E) None of these is correct.

Question 17

A body moving in simple harmonic motion has maximum acceleration when it has

Accepted Answer

A) maximum velocity. 
B) maximum kinetic energy. 
C) minimum potential energy. 
D) minimum kinetic energy. 
E) zero displacement. 
A) maximum velocity. 
B) maximum kinetic energy. 
C) minimum potential energy. 
D) minimum kinetic energy. 
E) zero displacement.

Question 18

The displacement of a body moving with simple harmonic motion is given by the equation   After one-quarter of a period has elapsed since t = 0,which of the following statements is correct?

Accepted Answer

A) Half the total energy of the body is kinetic energy and half is potential energy. 
B) The kinetic energy is a maximum. 
C) The potential energy is a maximum. 
D) The total energy is a negative maximum. 
E) Both kinetic and potential energies are maxima. 
A) Half the total energy of the body is kinetic energy and half is potential energy. 
B) The kinetic energy is a maximum. 
C) The potential energy is a maximum. 
D) The total energy is a negative maximum. 
E) Both kinetic and potential energies are maxima.

Question 19

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 20

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

Exam 14: Oscillations

An oscillator has a quality factor of 300.By what percentage does its energy decrease in each cycle?

In simple harmonic motion,the displacement x = A cos ω\omegaω t and the acceleration a = - ω\omegaω 2x.If A = 0.25 m and the period is 0.32 s,the acceleration when t = 0.12 s is

If F is the force,x the displacement,and k a particular constant,for simple harmonic motion we must have

An oscillator has a quality factor of 100.By what percentage does its energy decrease in each cycle?

The displacement in simple harmonic motion is a maximum when the

A 2.5-kg object is attached to a spring of force constant k = 4.5 kN/m.The spring is stretched 10 cm from equilibrium and released.What is the kinetic energy of the mass-spring system when the mass is 5.0 cm from its equilibrium position?

You want a mass that,when hung on the end of a spring,oscillates with a period of 1 s.If the spring has a spring constant of 10 N/m,the mass should be

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 10-kg block starts from rest at a vertical height of 1 m on a 30º frictionless inclined plane.If the block slides down the incline and then 20 m along a frictionless horizontal surface into a fixed spring with a force constant of 100 N/m,the spring is compressed approximately

A body of mass M is executing simple harmonic motion with an amplitude of 8.0 cm and a maximum acceleration of 100 cm/s2.When the displacement of this body from the equilibrium position is 6.0 cm,the magnitude of the acceleration is approximately

For a simple pendulum to have a period of 1 s it must have a length of

What is the amplitude after 1 s?

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

A body moving in simple harmonic motion has maximum acceleration when it has

The displacement of a body moving with simple harmonic motion is given by the equation After one-quarter of a period has elapsed since t = 0,which of the following statements is correct?

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

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In simple harmonic motion,the displacement x = A cos $\omega$ t and the acceleration a = - $\omega$ ²x.If A = 0.25 m and the period is 0.32 s,the acceleration when t = 0.12 s 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 M is executing simple harmonic motion with an amplitude of 8.0 cm and a maximum acceleration of 100 cm/s².When the displacement of this body from the equilibrium position is 6.0 cm,the magnitude of the acceleration is approximately

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