Question 1

A 0.25 kg harmonic oscillator has a total mechanical energy of $4.1 \mathrm {~J}$ If the oscillation amplitude is $20.0 \mathrm {~cm}$ what is the oscillation frequency?

Accepted Answer

A) 4.6 Hz 
B) 1.4 Hz 
C) 2.3 Hz 
D) 3.2 Hz 
A) 4.6 Hz 
B) 1.4 Hz 
C) 2.3 Hz 
D) 3.2 Hz

Question 2

An object is attached to a vertical spring and bobs up and down between points A and B.Where is the object located when its kinetic energy is a maximum?

Accepted Answer

A) at either A or B 
B) midway between A and B 
C) one-third of the way between A and B 
D) one-fourth of the way between A and B 
E) at none of the above points 
A) at either A or B 
B) midway between A and B 
C) one-third of the way between A and B 
D) one-fourth of the way between A and B 
E) at none of the above points

Question 3

A 0.250-kg stone is attached to an ideal spring and undergoes simple harmonic oscillations with a period of 0.640 s.What is the spring constant of the spring?

Accepted Answer

A) 2.45 N/m 
B) 12.1 N/m 
C) 24.1 N/m 
D) 0.102 N/m 
E) 0.610 N/m 
A) 2.45 N/m 
B) 12.1 N/m 
C) 24.1 N/m 
D) 0.102 N/m 
E) 0.610 N/m

Question 4

A simple pendulum having a bob of mass M has a period T.If you double M but change nothing else,what would be the new period?

Accepted Answer

A) 2T 
B) T $\sqrt { 2 }$ 
C) T 
D) T/ $\sqrt { 2 }$ 
E) T/2 
A) 2T 
B) T $\sqrt { 2 }$ 
C) T 
D) T/ $\sqrt { 2 }$ 
E) T/2

Question 5

The position of a cart that is oscillating on a spring is given by the equation x = (12.3 cm)cos[(1.26 s-1)t].When t = 0.805 s,what are the (a)velocity and (b)acceleration of the cart?

Accepted Answer

(a)-13.2 c

Question 6

A ball vibrates back and forth from the free end of an ideal spring having a spring constant of 20 N/m.If the amplitude of this motion is 0.30 m,what is the kinetic energy of the ball when it is 0.30 m from its equilibrium position?

Accepted Answer

A) 0.00 J 
B) 0.22 J 
C) 0.45 J 
D) 0.90 J 
E) 1.4 J 
A) 0.00 J 
B) 0.22 J 
C) 0.45 J 
D) 0.90 J 
E) 1.4 J

Question 7

A simple pendulum has a period T on Earth.If it were used on Planet X,where the free fall acceleration is 3 times what it is on Earth,what would its period be?

Accepted Answer

A) 3T 
B)  $\sqrt { 3 }$ T 
C) T 
D) T/ $\sqrt { 3 }$ 
E) T/3 
A) 3T 
B)  $\sqrt { 3 }$ T 
C) T 
D) T/ $\sqrt { 3 }$ 
E) T/3

Question 8

A 0.150-kg cart that is attached to an ideal spring with a spring constant of 3.58 N/m undergoes simple harmonic oscillations with an amplitude of 7.50 cm.What is the total mechanical energy of the system?

Accepted Answer

A) 0.0201 J 
B) 0.0101 J 
C) 0.269 J 
D) 0.134 J 
E) 0 J 
A) 0.0201 J 
B) 0.0101 J 
C) 0.269 J 
D) 0.134 J 
E) 0 J

Question 9

An object undergoing simple harmonic motion has a maximum displacement of $6.2 \mathrm {~m}$ at $t = 0.00 \mathrm {~s}$ If the angular frequency of oscillation is $1.6 \mathrm { rad } / \mathrm { s } \text {, }$ what is the object's displacement when $t = 3.5 \mathrm {~s} ?$

Accepted Answer

A) 4.8 m 
B) 5.6 m 
C) 3.7 m 
D) 3.1 m 
A) 4.8 m 
B) 5.6 m 
C) 3.7 m 
D) 3.1 m

Question 10

The position of an object that is oscillating on an ideal spring is given by x = (17.4 cm)cos[(5.46 s-1)t].Write an expression for the velocity of the object as a function of time using the sine function.

Accepted Answer

v = - (95.

Question 11

A 1.5-kg cart attached to an ideal spring with a spring constant of 20 N/m oscillates on a horizontal,frictionless track.At time t = 0.00 s,the cart is released from rest at position x = 10 cm from the equilibrium position.
(a)What is the frequency of the oscillations of the cart?
(b)Determine the maximum speed of the cart.Where does the maximum speed occur?
(c)Find the maximum acceleration of the mass.Where does the maximum acceleration occur?
(d)How much total energy does this oscillating system contain?
(e)Express the displacement as a function of time using a cosine function.

Accepted Answer

(a)0.58 Hz 
(b)0.37 m/s,at the

Question 12

A block attached to an ideal spring of spring constant 15 N/m executes simple harmonic motion on a frictionless horizontal surface.At time t = 0 s,the block has a displacement of -0.90 m, a velocity of -0.80 m/s, and an acceleration of +2.9 m/s2 .The mass of the block is closest to

Accepted Answer

A) 2.3 kg 
B) 2.6 kg 
C) 4.7 kg 
D) 9.4 kg 
A) 2.3 kg 
B) 2.6 kg 
C) 4.7 kg 
D) 9.4 kg

Question 13

When a laboratory sample of unknown mass is placed on a vertical spring-scale having a spring constant of 467 N/m,the system obeys the equation y = (4.4 cm)cos(33.3 s-1 t).What is the mass of this laboratory sample?

Accepted Answer

Question 14

Tarzan swings back and forth on a long vine.His friend Jane notices in amazement that he makes 30 complete swings in 2.4 minutes.
(a)What is the frequency (in hertz)of Tarzan's swing?
(b)How long is the vine he is using?

Accepted Answer

(a)0.21 Hz

Question 15

Two simple pendulums,A and B,are each 3.0 m long,and the period of pendulum A is T.Pendulum A is twice as heavy as pendulum B.What is the period of pendulum B?

Accepted Answer

A) T/ $\sqrt { 2 }$ 
B) T 
C) T $\sqrt { 2 }$ 
D) 2T 
E) T/2 
A) T/ $\sqrt { 2 }$ 
B) T 
C) T $\sqrt { 2 }$ 
D) 2T 
E) T/2

Question 16

A 0.39-kg block on a horizontal frictionless surface is attached to an ideal spring whose force constant (spring constant)is $$570 \mathrm {~N} / \mathrm { m } .$$ The block is pulled from its equilibrium position at x = 0.000 m to a displacement x = +0.080 m and is released from rest.The block then executes simple harmonic motion along the horizontal x-axis.When the position of the block is $x = 0.057 \mathrm {~m}$ its kinetic energy is closest to

Accepted Answer

A) 0.90 J. 
B) 0.84 J. 
C) 0.95 J. 
D) 1.0 J. 
E) 1.1 J. 
A) 0.90 J. 
B) 0.84 J. 
C) 0.95 J. 
D) 1.0 J. 
E) 1.1 J.

Question 17

A simple harmonic oscillator oscillates with frequency f when its amplitude is A.If the amplitude is now doubled to 2A,what is the new frequency?

Accepted Answer

A) 2f 
B) 4f 
C) f 
D) f/2 
E) f/4 
A) 2f 
B) 4f 
C) f 
D) f/2 
E) f/4

Question 18

A simple pendulum takes 2.00 s to make one compete swing.If we now triple the length,how long will it take for one complete swing?

Accepted Answer

A) 6.00 s 
B) 3.46 s 
C) 2.00 s 
D) 1.15 s 
E) 0.667 s 
A) 6.00 s 
B) 3.46 s 
C) 2.00 s 
D) 1.15 s 
E) 0.667 s

Question 19

A 3.42-kg stone hanging vertically from an ideal spring on the earth undergoes simple harmonic motion at a place where g = 9.80 m/s2.If the spring constant of the spring is $12 \mathrm {~N} / \mathrm { m }$ find the period of oscillation of this setup on a planet where g = 1.60 m/s2.

Accepted Answer

A) 3.35 s 
B) 2.51 s 
C) 4.36 s 
D) 5.70 s 
A) 3.35 s 
B) 2.51 s 
C) 4.36 s 
D) 5.70 s

Question 20

A 0.16-kg block on a horizontal frictionless surface is attached to an ideal spring whose force constant (spring constant)is 360 N/m.The block is pulled from its equilibrium position at x = 0.000 m to a position x = +0.080 m and is released from rest.The block then executes simple harmonic motion along the horizontal x-axis.When the position is x = -0.037 m,what is the acceleration of the block?

Accepted Answer

A) 83 m/s2 
B) 43 m/s2 
C) 64 m/s2 
D) 270 m/s2 
E) 370 m/s2 
A) 83 m/s2 
B) 43 m/s2 
C) 64 m/s2 
D) 270 m/s2 
E) 370 m/s2

Exam 20: Vibrational Motion

A 0.25 kg harmonic oscillator has a total mechanical energy of 4.1 J4.1 \mathrm {~J}4.1 J If the oscillation amplitude is 20.0 cm20.0 \mathrm {~cm}20.0 cm what is the oscillation frequency?

An object is attached to a vertical spring and bobs up and down between points A and B.Where is the object located when its kinetic energy is a maximum?

A 0.250-kg stone is attached to an ideal spring and undergoes simple harmonic oscillations with a period of 0.640 s.What is the spring constant of the spring?

A simple pendulum having a bob of mass M has a period T.If you double M but change nothing else,what would be the new period?

The position of a cart that is oscillating on a spring is given by the equation x = (12.3 cm)cos[(1.26 s-1)t].When t = 0.805 s,what are the (a)velocity and (b)acceleration of the cart?

A ball vibrates back and forth from the free end of an ideal spring having a spring constant of 20 N/m.If the amplitude of this motion is 0.30 m,what is the kinetic energy of the ball when it is 0.30 m from its equilibrium position?

A simple pendulum has a period T on Earth.If it were used on Planet X,where the free fall acceleration is 3 times what it is on Earth,what would its period be?

A 0.150-kg cart that is attached to an ideal spring with a spring constant of 3.58 N/m undergoes simple harmonic oscillations with an amplitude of 7.50 cm.What is the total mechanical energy of the system?

The position of an object that is oscillating on an ideal spring is given by x = (17.4 cm)cos[(5.46 s-1)t].Write an expression for the velocity of the object as a function of time using the sine function.

A block attached to an ideal spring of spring constant 15 N/m executes simple harmonic motion on a frictionless horizontal surface.At time t = 0 s,the block has a displacement of -0.90 m, a velocity of -0.80 m/s, and an acceleration of +2.9 m/s2 .The mass of the block is closest to

When a laboratory sample of unknown mass is placed on a vertical spring-scale having a spring constant of 467 N/m,the system obeys the equation y = (4.4 cm)cos(33.3 s-1 t).What is the mass of this laboratory sample?

Tarzan swings back and forth on a long vine.His friend Jane notices in amazement that he makes 30 complete swings in 2.4 minutes. (a)What is the frequency (in hertz)of Tarzan's swing? (b)How long is the vine he is using?

Two simple pendulums,A and B,are each 3.0 m long,and the period of pendulum A is T.Pendulum A is twice as heavy as pendulum B.What is the period of pendulum B?

A simple harmonic oscillator oscillates with frequency f when its amplitude is A.If the amplitude is now doubled to 2A,what is the new frequency?

A simple pendulum takes 2.00 s to make one compete swing.If we now triple the length,how long will it take for one complete swing?

A 3.42-kg stone hanging vertically from an ideal spring on the earth undergoes simple harmonic motion at a place where g = 9.80 m/s2.If the spring constant of the spring is 12 N/m12 \mathrm {~N} / \mathrm { m }12 N/m find the period of oscillation of this setup on a planet where g = 1.60 m/s2.

Introduction

Kinematics: Motion in One Dimension

Newtonian Mechanics

Applying Newtons Laws

Circular Motion

Impulse and Linear Momentum

Work and Energy

Extended Bodies at Rest

Rotational Motion

Gases

Static Fluids

Fluids in Motion

First Law of Thermodynamics

Second Law of Thermodynamics

Electric Charge force and Energy

The Electric Field

Dc Circuits

Magnetism

Electromagnetic Induction

Mechanical Waves

Reflection and Refraction

Mirrors and Lenses

Wave Optics

Electromagnetic Waves

Special Relativity

Quantum Optics

Atomic Physics

Nuclear Physics

Particle Physics

Filters

A 0.25 kg harmonic oscillator has a total mechanical energy of $4.1 \mathrm {~J}$ If the oscillation amplitude is $20.0 \mathrm {~cm}$ what is the oscillation frequency?

The position of a cart that is oscillating on a spring is given by the equation x = (12.3 cm)cos[(1.26 s^-1)t].When t = 0.805 s,what are the (a)velocity and (b)acceleration of the cart?

The position of an object that is oscillating on an ideal spring is given by x = (17.4 cm)cos[(5.46 s^-1)t].Write an expression for the velocity of the object as a function of time using the sine function.

A block attached to an ideal spring of spring constant 15 N/m executes simple harmonic motion on a frictionless horizontal surface.At time t = 0 s,the block has a displacement of -0.90 m, a velocity of -0.80 m/s, and an acceleration of +2.9 m/s² .The mass of the block is closest to

When a laboratory sample of unknown mass is placed on a vertical spring-scale having a spring constant of 467 N/m,the system obeys the equation y = (4.4 cm)cos(33.3 s^-1 t).What is the mass of this laboratory sample?

A 3.42-kg stone hanging vertically from an ideal spring on the earth undergoes simple harmonic motion at a place where g = 9.80 m/s².If the spring constant of the spring is $12 \mathrm {~N} / \mathrm { m }$ find the period of oscillation of this setup on a planet where g = 1.60 m/s².