Question 1

A thin test tube is partially filled with lead pellets so that it floats vertically in a fluid. When displaced slightly in the vertical direction, the tube undergoes SHM. In water the period is found to be 1.25 s, and when in an unknown fluid its period is 1.40 s. Use Archimedes' Principle to help you determine the density of the unknown liquid. (Density of water = 1 g/cm3)

Accepted Answer

A)  1.1 g/cm3  
B)  1.2 g/cm3  
C)  0.89 g/cm3  
D)  0.80 g/cm3  
E)  0.94 g/cm3

Question 2

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

Question 3

The top graph represents the variation of displacement with time for a particle executing simple harmonic motion. Which curve in the bottom graph represents the variation of acceleration with time for the same particle?

Accepted Answer

A)  1 
B)  2 
C)  3 
D)  4 
E)  None of these is correct.

Question 4

The frequency of a simple harmonic motion is 2.6 $\times$ 10-4 s-1. The oscillation starts (t = 0) when the displacement has its maximum positive value of 6.5 $\times$ 10-3 cm. The earliest possible time at which the particle can be found at x = -2.6 $\times$ 10-3 cm is

Accepted Answer

A)  7.1 $\times$ 10-6 s 
B)  1.2 $\times$ 10-5 s 
C)  1.1 $\times$ 10-4 s 
D)  1.1 $\times$ 10-3 s 
E)  4.2 $\times$ 10-3 s

Question 5

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%

Question 6

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 set into oscillation with an initial amplitude of A = 2 cm. 
-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

Question 7

The kinetic energy of a body executing simple harmonic motion is plotted against time expressed in terms of the period T. At t = 0, the displacement is zero. Which of the graphs most closely represents these conditions?

Accepted Answer

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

Question 8

What must be the length of a simple pendulum with a period of 2.0 s if g = 9.8 m/s2?

Accepted Answer

A)  99 cm 
B)  97 m 
C)  6.2 cm 
D)  3.1 m 
E)  2.0 m

Question 9

The displacement of a body moving with simple harmonic motion is given by the equation
Y = A sin(2$\pi$t +  $\pi$)
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.

Question 10

A spring is cut in half. The ratio of the force constant of one of the halves to the force constant of the original spring is

Accepted Answer

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

Question 11

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 set into oscillation with an initial amplitude of A = 2 cm. 
-The oscillation is

Accepted Answer

A)  very weakly damped. 
B)  weakly damped. 
C)  critically damped. 
D)  overdamped. 
E)  unable to tell

Question 12

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

Question 13

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

Question 14

A light spring stretches 0.13 m when a 0.35 kg mass is hung from it. The mass is pulled down from this equilibrium position an additional 0.15 m and then released. Determine the maximum speed of the mass.

Accepted Answer

A)  1.10 m/s 
B)  2.75 m/s 
C)  11.4 m/s 
D)  1.25 m/s 
E)  0.02 m/s

Question 15

A body of mass M suspended from a spring oscillates with a period T. If the mass of the spring can be neglected, a body of mass 2M, suspended from the same spring, oscillates with a period of

Accepted Answer

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

Question 16

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.

Question 17

The energy of a simple harmonic oscillator could be doubled by increasing the amplitude by a factor of

Accepted Answer

A)  0.7 
B)  1.0 
C)  1.4 
D)  2.0 
E)  4.0

Question 18

The energy of an oscillator decreases by 10% each cycle. The quality factor of this oscillator is approximately

Accepted Answer

A)  314 
B)  157 
C)  87 
D)  63 
E)  21

Question 19

Any body moving with simple harmonic motion is being acted on by a force that is

Accepted Answer

A)  constant. 
B)  proportional to a sine or cosine function of the displacement. 
C)  proportional to the inverse square of the displacement. 
D)  directly proportional to the displacement. 
E)  proportional to the square of the displacement.

Question 20

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.

Exam 14: Oscillations

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

The top graph represents the variation of displacement with time for a particle executing simple harmonic motion. Which curve in the bottom graph represents the variation of acceleration with time for the same particle?

The frequency of a simple harmonic motion is 2.6 $\times$ 10^-4 s^-1. The oscillation starts (t = 0) when the displacement has its maximum positive value of 6.5 $\times$ 10^-3 cm. The earliest possible time at which the particle can be found at x = -2.6 $\times$ 10^-3 cm is

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

The kinetic energy of a body executing simple harmonic motion is plotted against time expressed in terms of the period T. At t = 0, the displacement is zero. Which of the graphs most closely represents these conditions?

What must be the length of a simple pendulum with a period of 2.0 s if g = 9.8 m/s²?

A spring is cut in half. The ratio of the force constant of one of the halves to the force constant of the original spring is

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?

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?

A light spring stretches 0.13 m when a 0.35 kg mass is hung from it. The mass is pulled down from this equilibrium position an additional 0.15 m and then released. Determine the maximum speed of the mass.

A body of mass M suspended from a spring oscillates with a period T. If the mass of the spring can be neglected, a body of mass 2M, suspended from the same spring, oscillates with a period of

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

The energy of a simple harmonic oscillator could be doubled by increasing the amplitude by a factor of

The energy of an oscillator decreases by 10% each cycle. The quality factor of this oscillator is approximately

Any body moving with simple harmonic motion is being acted on by a force that is

Exam 14: Oscillations

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

The top graph represents the variation of displacement with time for a particle executing simple harmonic motion. Which curve in the bottom graph represents the variation of acceleration with time for the same particle?

The frequency of a simple harmonic motion is 2.6 ×\times× 10-4 s-1. The oscillation starts (t = 0) when the displacement has its maximum positive value of 6.5 ×\times× 10-3 cm. The earliest possible time at which the particle can be found at x = -2.6 ×\times× 10-3 cm is

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

The kinetic energy of a body executing simple harmonic motion is plotted against time expressed in terms of the period T. At t = 0, the displacement is zero. Which of the graphs most closely represents these conditions?

What must be the length of a simple pendulum with a period of 2.0 s if g = 9.8 m/s2?

The displacement of a body moving with simple harmonic motion is given by the equation Y = A sin(2 π\piπ t + π\piπ ) After one-quarter of a period has elapsed since t = 0, which of the following statements is correct?

A spring is cut in half. The ratio of the force constant of one of the halves to the force constant of the original spring is

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?

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?

A light spring stretches 0.13 m when a 0.35 kg mass is hung from it. The mass is pulled down from this equilibrium position an additional 0.15 m and then released. Determine the maximum speed of the mass.

A body of mass M suspended from a spring oscillates with a period T. If the mass of the spring can be neglected, a body of mass 2M, suspended from the same spring, oscillates with a period of

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

The energy of a simple harmonic oscillator could be doubled by increasing the amplitude by a factor of

The energy of an oscillator decreases by 10% each cycle. The quality factor of this oscillator is approximately

Any body moving with simple harmonic motion is being acted on by a force that 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 frequency of a simple harmonic motion is 2.6 $\times$ 10^-4 s^-1. The oscillation starts (t = 0) when the displacement has its maximum positive value of 6.5 $\times$ 10^-3 cm. The earliest possible time at which the particle can be found at x = -2.6 $\times$ 10^-3 cm is

What must be the length of a simple pendulum with a period of 2.0 s if g = 9.8 m/s²?