Question 1

A large spring requires a force of 100 N to compress it only 0.010 m. What is the spring constant of the spring?

Accepted Answer

A)  1.0 N/m 
B)  100 N/m 
C)  10,000 N/m 
D)  100,000 N/m 
A)  1.0 N/m 
B)  100 N/m 
C)  10,000 N/m 
D)  100,000 N/m

Question 2

The motion of a piston in an automobile engine is nearly simple harmonic. If the 1-kg piston travels back and forth over a distance of 12.0 cm, what is its maximum speed when the engine is running at 3000 rpm?

Accepted Answer

A)  4.71 m/s 
B)  9.42 m/s 
C)  44.0m/s 
D)  22.0 m/s 
A)  4.71 m/s 
B)  9.42 m/s 
C)  44.0m/s 
D)  22.0 m/s

Question 3

A mass on a spring vibrates in simple harmonic motion at a frequency of 4.0 Hz and an amplitude of 8.0 cm. If a timer is started when its displacement from equilibrium is a maximum (hence x = 8 cm when t = 0), what is the displacement of the mass when t = 3.7 s?

Accepted Answer

A)  zero 
B)  0.025 m 
C)  0.049 m 
D)  0.080 m 
A)  zero 
B)  0.025 m 
C)  0.049 m 
D)  0.080 m

Question 4

A 2.0 cm   2.0 cm steel rod of length 80 cm has its left end clamped and a force of   applied perpendicular to its length at its right end. By how much does the right end shift from its original position? For steel Young's modulus is   , the bulk modulus is   , and the shear modulus is   .

Accepted Answer

A)    
B)    
C)    
D)  More information is needed. 
A)    
B)    
C)    
D)  More information is needed.

Question 5

The position of a 0.64-kg mass undergoing simple harmonic motion is given by x = (0.160 m) cos ( $\pi$t/8). What is its period of oscillation?

Accepted Answer

A)  100 s 
B)  32 s 
C)  16 s 
D)  8.0 s 
A)  100 s 
B)  32 s 
C)  16 s 
D)  8.0 s

Question 6

A simple pendulum has a mass of 0.50 kg and a length of 1.0 m. It is displaced through an angle of 30$\degree$ and then released. After a time, the maximum angle of swing is only 10$\degree$. How much energy has been lost to friction?

Accepted Answer

A)  2.0 J 
B)  1.6 J 
C)  0.66 J 
D)  0.58 J 
A)  2.0 J 
B)  1.6 J 
C)  0.66 J 
D)  0.58 J

Question 7

The SI base units for the spring constant are which of the following?

Accepted Answer

A)  kg·s2 
B)  kg/m2 
C)  kg/s2 
D)  kg·m2 
A)  kg·s2 
B)  kg/m2 
C)  kg/s2 
D)  kg·m2

Question 8

Suppose a 0.30-kg mass on a spring that has been compressed 0.10 m has elastic potential energy of 1.5 J. What is the spring constant?

Accepted Answer

A)  10 N/m 
B)  20 N/m 
C)  200 N/m 
D)  300 N/m 
A)  10 N/m 
B)  20 N/m 
C)  200 N/m 
D)  300 N/m

Question 9

If one could transport a simple pendulum of constant length from the Earth's surface to the Moon's, where the acceleration due to gravity is one-sixth (1/6) that on the Earth, by what factor would the pendulum frequency be changed?

Accepted Answer

A)  about 6.0 
B)  about 2.5 
C)  about 0.41 
D)  about 0.17 
A)  about 6.0 
B)  about 2.5 
C)  about 0.41 
D)  about 0.17

Question 10

Three identical springs, each with spring constant k, are attached in parallel to a mass, which is then set into simple harmonic motion. What would be the spring constant of a single spring which would result in the same frequency of oscillation as the parallel springs?

Accepted Answer

A)  k 
B)  k/3 
C)  3k 
D)    
A)  k 
B)  k/3 
C)  3k 
D)

Question 11

The oxygen molecule (O2) may be regarded as two masses connected by a spring. In vibrational motion, each oxygen atom alternately approaches, then moves away from the center of mass of the system. If each oxygen atom of mass m = 2.67 *10 - 26 kg has a vibrational energy of 6.4 * 10-21 J and the effective spring constant is 50 N/m, then what is the amplitude of oscillation of each oxygen atom?

Accepted Answer

A)  3.2 *10-11 m 
B)  1.6 *10-11 m 
C)  1.1 * 10-11 m 
D)  8.0 *10-12 m 
A)  3.2 *10-11 m 
B)  1.6 *10-11 m 
C)  1.1 * 10-11 m 
D)  8.0 *10-12 m

Question 12

A mass on a spring vibrates in simple harmonic motion at a frequency of 4.0 Hz and an amplitude of 4.0 cm. If a timer is started when its displacement is a maximum (hence x = 4 cm when t = 0), what is the speed of the mass when t = 5 s?

Accepted Answer

A)  zero 
B)  0.0065 m/s 
C)  0.016 m/s 
D)  0.024 m/s 
A)  zero 
B)  0.0065 m/s 
C)  0.016 m/s 
D)  0.024 m/s

Question 13

When water freezes, it expands about nine percent. What would be the pressure increase inside your automobile engine block if the water in there froze? (The bulk modulus of ice is 2.0 *109 Pa, and 1 atm = 1.0 *105 Pa.)

Accepted Answer

A)  18 atm 
B)  270 atm 
C)  1080 atm 
D)  1800 atm 
A)  18 atm 
B)  270 atm 
C)  1080 atm 
D)  1800 atm

Question 14

The quantity "strain" expressed in terms of the fundamental quantities (mass, length, time) is equivalent to:

Accepted Answer

A)  MLT - 1. 
B)  ML - 1T - 2. 
C)  M2L - 1T - 3. 
D)  a dimensionless quantity. 
A)  MLT - 1. 
B)  ML - 1T - 2. 
C)  M2L - 1T - 3. 
D)  a dimensionless quantity.

Question 15

Suppose a simple harmonic oscillator has a frequency 20 Hz. What is frequency of occurrence of the maximum kinetic energy during its oscillations?

Accepted Answer

A)  20 Hz 
B)    Hz 
C)  10 Hz 
D)  40 Hz 
A)  20 Hz 
B)    Hz 
C)  10 Hz 
D)  40 Hz

Question 16

Suppose a 0.30-kg mass on a spring that has been compressed 0.20 m has elastic potential energy of 1.0 J. How much further must the spring be compressed to triple the elastic potential energy?

Accepted Answer

A)  0.35 m 
B)  0.15 m 
C)  0.10 m 
D)  0.05 m 
A)  0.35 m 
B)  0.15 m 
C)  0.10 m 
D)  0.05 m

Question 17

Which is not an example of approximate simple harmonic motion?

Accepted Answer

A)  A ball bouncing on the floor. 
B)  A child swinging on a swing. 
C)  A piano string that has been struck. 
D)  A car's radio antenna as it waves back and forth. 
A)  A ball bouncing on the floor. 
B)  A child swinging on a swing. 
C)  A piano string that has been struck. 
D)  A car's radio antenna as it waves back and forth.

Question 18

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. What is the speed of the block when it passes through the equilibrium point?

Accepted Answer

A)  2.1 m/s 
B)  1.6 m/s 
C)  0.80 m/s 
D)  0.57 m/s 
A)  2.1 m/s 
B)  1.6 m/s 
C)  0.80 m/s 
D)  0.57 m/s

Question 19

A mass of 4.0 kg, resting on a horizontal, frictionless surface, is attached on the right to a horizontal spring with spring constant 30 N/m and on the left to a horizontal spring with spring constant 50 N/m. If this system is moved from equilibrium, what is the effective spring constant?

Accepted Answer

A)  "16 N/m" 
B)  "80 N/m" 
C)  "20 N/m" 
D)  "-20 N/m" 
A)  "16 N/m" 
B)  "80 N/m" 
C)  "20 N/m" 
D)  "-20 N/m"

Question 20

A 0.40-kg object, attached to a spring with spring constant k = 10 N/m, is moving on a horizontal, frictionless surface in simple harmonic motion of amplitude of 0.080 m. What is its speed at the instant when its displacement is 0.040 m? (Hint: Use conservation of energy.)

Accepted Answer

A)  17 m/s 
B)  35 cm/s 
C)  3.5 cm/s 
D)  6.9 cm/s 
A)  17 m/s 
B)  35 cm/s 
C)  3.5 cm/s 
D)  6.9 cm/s

Exam 11: Harmonic Motion and Elasticity

A large spring requires a force of 100 N to compress it only 0.010 m. What is the spring constant of the spring?

The motion of a piston in an automobile engine is nearly simple harmonic. If the 1-kg piston travels back and forth over a distance of 12.0 cm, what is its maximum speed when the engine is running at 3000 rpm?

A mass on a spring vibrates in simple harmonic motion at a frequency of 4.0 Hz and an amplitude of 8.0 cm. If a timer is started when its displacement from equilibrium is a maximum (hence x = 8 cm when t = 0), what is the displacement of the mass when t = 3.7 s?

A 2.0 cm 2.0 cm steel rod of length 80 cm has its left end clamped and a force of applied perpendicular to its length at its right end. By how much does the right end shift from its original position? For steel Young's modulus is , the bulk modulus is , and the shear modulus is .

The position of a 0.64-kg mass undergoing simple harmonic motion is given by x = (0.160 m) cos ( π\piπ t/8). What is its period of oscillation?

A simple pendulum has a mass of 0.50 kg and a length of 1.0 m. It is displaced through an angle of 30 °\degree° and then released. After a time, the maximum angle of swing is only 10 °\degree° . How much energy has been lost to friction?

The SI base units for the spring constant are which of the following?

Suppose a 0.30-kg mass on a spring that has been compressed 0.10 m has elastic potential energy of 1.5 J. What is the spring constant?

If one could transport a simple pendulum of constant length from the Earth's surface to the Moon's, where the acceleration due to gravity is one-sixth (1/6) that on the Earth, by what factor would the pendulum frequency be changed?

Three identical springs, each with spring constant k, are attached in parallel to a mass, which is then set into simple harmonic motion. What would be the spring constant of a single spring which would result in the same frequency of oscillation as the parallel springs?

A mass on a spring vibrates in simple harmonic motion at a frequency of 4.0 Hz and an amplitude of 4.0 cm. If a timer is started when its displacement is a maximum (hence x = 4 cm when t = 0), what is the speed of the mass when t = 5 s?

When water freezes, it expands about nine percent. What would be the pressure increase inside your automobile engine block if the water in there froze? (The bulk modulus of ice is 2.0 *109 Pa, and 1 atm = 1.0 *105 Pa.)

The quantity "strain" expressed in terms of the fundamental quantities (mass, length, time) is equivalent to:

Suppose a simple harmonic oscillator has a frequency 20 Hz. What is frequency of occurrence of the maximum kinetic energy during its oscillations?

Suppose a 0.30-kg mass on a spring that has been compressed 0.20 m has elastic potential energy of 1.0 J. How much further must the spring be compressed to triple the elastic potential energy?

Which is not an example of approximate simple harmonic motion?

A mass of 4.0 kg, resting on a horizontal, frictionless surface, is attached on the right to a horizontal spring with spring constant 30 N/m and on the left to a horizontal spring with spring constant 50 N/m. If this system is moved from equilibrium, what is the effective spring constant?

A 0.40-kg object, attached to a spring with spring constant k = 10 N/m, is moving on a horizontal, frictionless surface in simple harmonic motion of amplitude of 0.080 m. What is its speed at the instant when its displacement is 0.040 m? (Hint: Use conservation of energy.)

Introduction

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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/8). What is its period of oscillation?

A simple pendulum has a mass of 0.50 kg and a length of 1.0 m. It is displaced through an angle of 30 $\degree$ and then released. After a time, the maximum angle of swing is only 10 $\degree$ . How much energy has been lost to friction?

When water freezes, it expands about nine percent. What would be the pressure increase inside your automobile engine block if the water in there froze? (The bulk modulus of ice is 2.0 10⁹ Pa, and 1 atm = 1.0 10⁵ Pa.)