Question 1

The position of a 0.64-kg mass undergoing simple harmonic motion is given by x = (0.160 m) cos ( $\pi$t/16). What is its position at t = 6.0 s?

Accepted Answer

A)  0.160 m 
B)  0.159 m 
C)  0.061 m 
D)  0.089 m 
A)  0.160 m 
B)  0.159 m 
C)  0.061 m 
D)  0.089 m C

Question 2

A 0.20-kg object is attached to a spring with spring constant k = 10 N/m and moves with simple harmonic motion over a horizontal, frictionless surface. At the instant that it is displaced from equilibrium by -0.060 m, what is its acceleration?

Accepted Answer

A)  "360 m/s2" 
B)  "-30 m/s2" 
C)  "3.0 m/s2" 
D)  "0.18 m/s2" 
A)  "360 m/s2" 
B)  "-30 m/s2" 
C)  "3.0 m/s2" 
D)  "0.18 m/s2" C

Question 3

A copper alloy wire of length 2.0 m, cross sectional area 7.1 *10-6 m2, and Young's modulus 11 *1010 N/m2, has a 200-kg load hung on it. What is its increase in length? (g = 9.8 m/s2)

Accepted Answer

A)  0.50 mm 
B)  1.0 mm 
C)  2.5 mm 
D)  5.0 mm 
A)  0.50 mm 
B)  1.0 mm 
C)  2.5 mm 
D)  5.0 mm D

Question 4

An ore car of mass 2000 kg rolls downhill on tracks from a mine. At the end of the tracks, 10.0 m lower in elevation, is a spring with k = 400,000 N/m. How much is the spring compressed in stopping the ore car? Ignore friction.

Accepted Answer

A)  0.14 m 
B)  0.99 m 
C)  1.40 m 
D)  1.96 m 
A)  0.14 m 
B)  0.99 m 
C)  1.40 m 
D)  1.96 m

Question 5

To double the total energy of a simple harmonic oscillator, by what factor should the amplitude change?

Accepted Answer

A)  2 
B)    
C)  4 
D)    
A)  2 
B)    
C)  4 
D)

Question 6

A simple pendulum has a period of 1.0 s. What is the pendulum length? (g = 9.8 m/s2)

Accepted Answer

A)  0.25 m 
B)  0.39 m 
C)  0.99 m 
D)  1.0 m 
A)  0.25 m 
B)  0.39 m 
C)  0.99 m 
D)  1.0 m

Question 7

A tiny spring, with a spring constant of 1.20 N/m, will be stretched to what displacement by a 0.0060-N force?

Accepted Answer

A)  4.2 mm 
B)  5.0 mm 
C)  6.0 mm 
D)  9.4 mm 
A)  4.2 mm 
B)  5.0 mm 
C)  6.0 mm 
D)  9.4 mm

Question 8

Four identical springs each have the same spring constant k. If these four springs are attached end to end forming a spring four times the length of one of the original springs, what will be the spring constant of the combination?

Accepted Answer

A)  k 
B)  k/4 
C)  4k 
D)  1.41k 
A)  k 
B)  k/4 
C)  4k 
D)  1.41k

Question 9

A mass of 0.40 kg, hanging from a spring with a spring constant of 160 N/m, is set into an up-and-down simple harmonic motion. What is the speed of the mass when moving through the equilibrium point? The starting displacement from equilibrium is 0.10 m.

Accepted Answer

A)  zero 
B)  1.4 m/s 
C)  2.0 m/s 
D)  3.4 m/s 
A)  zero 
B)  1.4 m/s 
C)  2.0 m/s 
D)  3.4 m/s

Question 10

A 0.20-kg block rests on a frictionless, level surface and is attached to a horizontally aligned spring with a spring constant of 80 N/m. The block is initially displaced 4.0 cm from the equilibrium point and then released to set up a simple harmonic motion. A frictional force of 0.3 N exists between the block and surface. What is the speed of the block when it passes through the equilibrium point after being released from the 4.0-cm displacement point?

Accepted Answer

A)  0.45 m/s 
B)  0.63 m/s 
C)  0.72 m/s 
D)  1.2 m/s 
A)  0.45 m/s 
B)  0.63 m/s 
C)  0.72 m/s 
D)  1.2 m/s

Question 11

When car shock absorbers wear out and lose their damping ability, what is the resulting oscillating behavior?

Accepted Answer

A)  underdamped 
B)  critically damped 
C)  overdamped 
D)  hyperdamped 
A)  underdamped 
B)  critically damped 
C)  overdamped 
D)  hyperdamped

Question 12

The position of a 0.64-kg mass undergoing simple harmonic motion is given by x = (0.120 m) cos ( $\pi$t/16). What is the maximum net force on the mass as it oscillates?

Accepted Answer

A)  0.98 *10-3 N 
B)  7.4 *10-3 N 
C)  3.0 * 10-3 N 
D)  4.7 N 
A)  0.98 *10-3 N 
B)  7.4 *10-3 N 
C)  3.0 * 10-3 N 
D)  4.7 N

Question 13

By what factor must one change the weight suspended vertically from a spring coil in order to double its period of simple harmonic motion?

Accepted Answer

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

Question 14

What are the base SI units for the torsion constant   ?

Accepted Answer

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

Question 15

Doubling the weight suspended vertically from a coil spring will result in a change in the displacement of the spring's lower end by what factor?

Accepted Answer

A)  4.0 
B)  3.0 
C)  2.0 
D)  0.5 
A)  4.0 
B)  3.0 
C)  2.0 
D)  0.5

Question 16

The kinetic energy of the bob on a simple pendulum swinging in simple harmonic motion has its maximum value when the displacement from equilibrium is at what point in its swing?

Accepted Answer

A)  zero displacement 
B)  1/4 the amplitude 
C)  1/2 the amplitude 
D)  equal the amplitude 
A)  zero displacement 
B)  1/4 the amplitude 
C)  1/2 the amplitude 
D)  equal the amplitude

Question 17

A mass on a spring vibrates in simple harmonic motion at a frequency of 4.0 Hz and an amplitude of 5.0 cm. If a timer is started when its displacement is a maximum (hence x = 5 cm when t = 0), what is the acceleration magnitude when t = 3 s?

Accepted Answer

A)  31.6 m/s2 
B)  15.8 m/s2 
C)  10.5 m/s2 
D)  zero 
A)  31.6 m/s2 
B)  15.8 m/s2 
C)  10.5 m/s2 
D)  zero

Question 18

A car with bad shocks bounces up and down with a period of 1.50 s after hitting a bump. The car has a mass of 1250 kg and is supported by four springs of force constant k. What is k for each spring?

Accepted Answer

A)  6580 N/m 
B)  5480 N/m 
C)  4440 N/m 
D)  3630 N/m 
A)  6580 N/m 
B)  5480 N/m 
C)  4440 N/m 
D)  3630 N/m

Question 19

A runaway railroad car, with mass 30 *104 kg, coasts across a level track at 2.0 m/s when it collides with a spring-loaded bumper at the end of the track. If the spring constant of the bumper is 4.0 *106 N/m, what is the maximum compression of the spring during the collision? (Assume the collision is elastic.)

Accepted Answer

A)  0.77 m 
B)  0.55 m 
C)  0.34 m 
D)  1.07 m 
A)  0.77 m 
B)  0.55 m 
C)  0.34 m 
D)  1.07 m

Question 20

A mass on a spring vibrates in simple harmonic motion at a frequency of 4.0 Hz and amplitude of 8.0 cm. If the mass of the object is 0.25 kg, what is the spring constant?

Accepted Answer

A)  40 N/m 
B)  87 N/m 
C)  126 N/m 
D)  158 N/m 
A)  40 N/m 
B)  87 N/m 
C)  126 N/m 
D)  158 N/m

Exam 11: Harmonic Motion and Elasticity

The position of a 0.64-kg mass undergoing simple harmonic motion is given by x = (0.160 m) cos ( π\piπ t/16). What is its position at t = 6.0 s?

A 0.20-kg object is attached to a spring with spring constant k = 10 N/m and moves with simple harmonic motion over a horizontal, frictionless surface. At the instant that it is displaced from equilibrium by -0.060 m, what is its acceleration?

A copper alloy wire of length 2.0 m, cross sectional area 7.1 *10-6 m2, and Young's modulus 11 *1010 N/m2, has a 200-kg load hung on it. What is its increase in length? (g = 9.8 m/s2)

An ore car of mass 2000 kg rolls downhill on tracks from a mine. At the end of the tracks, 10.0 m lower in elevation, is a spring with k = 400,000 N/m. How much is the spring compressed in stopping the ore car? Ignore friction.

To double the total energy of a simple harmonic oscillator, by what factor should the amplitude change?

A simple pendulum has a period of 1.0 s. What is the pendulum length? (g = 9.8 m/s2)

A tiny spring, with a spring constant of 1.20 N/m, will be stretched to what displacement by a 0.0060-N force?

Four identical springs each have the same spring constant k. If these four springs are attached end to end forming a spring four times the length of one of the original springs, what will be the spring constant of the combination?

A mass of 0.40 kg, hanging from a spring with a spring constant of 160 N/m, is set into an up-and-down simple harmonic motion. What is the speed of the mass when moving through the equilibrium point? The starting displacement from equilibrium is 0.10 m.

When car shock absorbers wear out and lose their damping ability, what is the resulting oscillating behavior?

The position of a 0.64-kg mass undergoing simple harmonic motion is given by x = (0.120 m) cos ( π\piπ t/16). What is the maximum net force on the mass as it oscillates?

By what factor must one change the weight suspended vertically from a spring coil in order to double its period of simple harmonic motion?

What are the base SI units for the torsion constant ?

Doubling the weight suspended vertically from a coil spring will result in a change in the displacement of the spring's lower end by what factor?

The kinetic energy of the bob on a simple pendulum swinging in simple harmonic motion has its maximum value when the displacement from equilibrium is at what point in its swing?

A mass on a spring vibrates in simple harmonic motion at a frequency of 4.0 Hz and an amplitude of 5.0 cm. If a timer is started when its displacement is a maximum (hence x = 5 cm when t = 0), what is the acceleration magnitude when t = 3 s?

A car with bad shocks bounces up and down with a period of 1.50 s after hitting a bump. The car has a mass of 1250 kg and is supported by four springs of force constant k. What is k for each spring?

A mass on a spring vibrates in simple harmonic motion at a frequency of 4.0 Hz and amplitude of 8.0 cm. If the mass of the object is 0.25 kg, what is the spring constant?

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Filters

The position of a 0.64-kg mass undergoing simple harmonic motion is given by x = (0.160 m) cos ( $\pi$ t/16). What is its position at t = 6.0 s?

A copper alloy wire of length 2.0 m, cross sectional area 7.1 10^-⁶ m², and Young's modulus 11 10¹⁰ N/m², has a 200-kg load hung on it. What is its increase in length? (g = 9.8 m/s²)

A simple pendulum has a period of 1.0 s. What is the pendulum length? (g = 9.8 m/s²)

The position of a 0.64-kg mass undergoing simple harmonic motion is given by x = (0.120 m) cos ( $\pi$ t/16). What is the maximum net force on the mass as it oscillates?