Question 1

A mass M is attached to an ideal massless spring. When this system is set in motion, it has a period T. What is the period if the mass is doubled to 2M?

Accepted Answer

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

Question 2

In designing buildings to be erected in an area prone to earthquakes, what relationship should the designer try to achieve between the natural frequency of the building and the typical earthquake frequencies?

Accepted Answer

A)  The natural frequency of the building should be exactly the same as typical earthquake frequencies. 
B)  The natural frequency of the building should be very different from typical earthquake frequencies. 
C)  The natural frequency of the building should be almost the same as typical earthquake frequencies but slightly higher. 
D)  The natural frequency of the building should be almost the same as typical earthquake frequencies but slightly lower. 
A)  The natural frequency of the building should be exactly the same as typical earthquake frequencies. 
B)  The natural frequency of the building should be very different from typical earthquake frequencies. 
C)  The natural frequency of the building should be almost the same as typical earthquake frequencies but slightly higher. 
D)  The natural frequency of the building should be almost the same as typical earthquake frequencies but slightly lower. B

Question 3

A 0.50-kg object is attached to an ideal massless spring of spring constant 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position.
(a) What is the amplitude of vibration?
(b) At what location are the kinetic energy and the potential energy of the system the same?

Accepted Answer

(a) 0.24 m 
(b) x = 0.17 m

Question 4

A frictionless pendulum released from 65 degrees with the vertical will vibrate with the same frequency as if it were released from 5 degrees with the vertical because the period is independent of the amplitude and mass.

Accepted Answer

A) True 
 B)False

Question 5

A 12.0-N object is oscillating in simple harmonic motion at the end of an ideal vertical spring. Its vertical position y as a function of time t is given by y(t) = 4.50 cm cos[(19.5 s-1)t - π/8].
(a) What is the spring constant of the spring?
(b) What is the maximum acceleration of the object?
(c) What is the maximum speed that the object reaches?
(d) How long does it take the object to go from its highest point to its lowest point?

Accepted Answer

(a) 466 N/m 
(b) 17.

Question 6

A frictionless simple pendulum on Earth has a period of 1.75 s. On Planet X its period is 2.14 s. What is the acceleration due to gravity on Planet X?

Accepted Answer

The answer of A frictionless simple pendulum on Earth has...

Question 7

In the figure, two masses, M = 16 kg and m = 12.8.0 kg, are connected to a very light rigid bar and are attached to an ideal massless spring of spring constant 100 N/m. The system is set into oscillation with an amplitude of 78 cm. At the instant when the acceleration is at its maximum, the 16-kg mass separates from the 12.8.0-kg mass, which then remains attached to the spring and continues to oscillate. What will be the amplitude of oscillation of the 12.8.0-kg mass?

Accepted Answer

A)  78 cm 
B)  62 cm 
C)  35 cm 
D)  98 cm 
E)  180 cm 
A)  78 cm 
B)  62 cm 
C)  35 cm 
D)  98 cm 
E)  180 cm

Question 8

If we double only the amplitude of a vibrating ideal mass-and-spring system, the mechanical energy of the system

Accepted Answer

A)  increases by a factor of   . 
B)  increases by a factor of 2. 
C)  increases by a factor of 3. 
D)  increases by a factor of 4. 
E)  does not change. 
A)  increases by a factor of   . 
B)  increases by a factor of 2. 
C)  increases by a factor of 3. 
D)  increases by a factor of 4. 
E)  does not change.

Question 9

An object of mass 8.0 kg is attached to an ideal massless spring and allowed to hang in the Earth's gravitational field. The spring stretches 3.6 cm before it reaches its equilibrium position. If this system is allowed to oscillate, what will be its frequency?

Accepted Answer

A)  2.6 Hz 
B)  0.0045 Hz 
C)  0.67 Hz 
D)  2.1 Hz 
A)  2.6 Hz 
B)  0.0045 Hz 
C)  0.67 Hz 
D)  2.1 Hz

Question 10

The amplitude of a lightly damped harmonic oscillator decreases from 60.0 cm to 40.0 cm in 10.0 s. What will be the amplitude of the harmonic oscillator after another 10.0 s passes?

Accepted Answer

A)  20.0 cm 
B)  167 cm 
C)  30.0 cm 
D)  0.00 cm 
E)  26.7 cm 
A)  20.0 cm 
B)  167 cm 
C)  30.0 cm 
D)  0.00 cm 
E)  26.7 cm

Question 11

An object is attached to a vertical ideal massless spring and bobs up and down between the two extreme points A and B. When the kinetic energy of the object is a minimum, the object is located

Accepted Answer

A)  at either A or B. 
B)  midway between A and B. 
C)  1/3 of the distance from A to B. 
D)  1/4 of the distance from A to B. 
E)  1/   times the distance from A to B. 
A)  at either A or B. 
B)  midway between A and B. 
C)  1/3 of the distance from A to B. 
D)  1/4 of the distance from A to B. 
E)  1/   times the distance from A to B.

Question 12

A 2.15 kg lightly damped harmonic oscillator has an angular oscillation frequency of 0.261 rad/s. If the maximum displacement of 2.0 m occurs when t = 0.00 s, and the damping constant b is 0.74 kg/s what is the object's displacement when t = 4.01 s?

Accepted Answer

A)  0.50 m 
B)  0.43 m 
C)  0.58 m 
D)  0.65 m 
A)  0.50 m 
B)  0.43 m 
C)  0.58 m 
D)  0.65 m

Question 13

The x component of the velocity of an object vibrating along the x-axis obeys the equation vx(t) = (0.445 m/s) sin[(25.4 rad/s)t + 0.223].
(a) What is the amplitude of the motion of this object?
(b) What is the maximum acceleration of the vibrating object?

Accepted Answer

(a) 0.0175

Question 14

A sewing machine needle moves up and down in simple harmonic motion with an amplitude of 1.27 cm and a frequency of 2.55 Hz.
(a) What is the maximum speed of the needle?
(b) What is the maximum acceleration of the needle?

Accepted Answer

(a) 20.3 c

Question 15

A large stick is pivoted about one end and allowed to swing back and forth with no friction as a physical pendulum. The mass of the stick is 5.40 kg and its center of gravity (found by finding its balance point) is 1.80 m from the pivot. If the period of the swinging stick is 6.90 seconds, what is the moment of inertia of the stick about an axis through the pivot?

Accepted Answer

The answer of A large stick is pivoted about one...

Question 16

The simple harmonic motion of an object is described by the graph shown in the figure. What is the equation for the position x(t) of the object as a function of time t?

Accepted Answer

A)  x(t) = (4.0 m)sin[(2π/8.0 s)t + π/3.0] 
B)  x(t) = (4.0 m)cos[(2π/8.0 s)t + 2π/3.0] 
C)  x(t) = (4.0 m)cos[(2π/8.0 s)t + π/3.0] 
D)  x(t) = (4.0 m)cos[(2π/8.0 s)t - π/3.0] 
E)  x(t) = (8.0 m)cos[(2π/8.0 s)t + π/3.0] 
A)  x(t) = (4.0 m)sin[(2π/8.0 s)t + π/3.0] 
B)  x(t) = (4.0 m)cos[(2π/8.0 s)t + 2π/3.0] 
C)  x(t) = (4.0 m)cos[(2π/8.0 s)t + π/3.0] 
D)  x(t) = (4.0 m)cos[(2π/8.0 s)t - π/3.0] 
E)  x(t) = (8.0 m)cos[(2π/8.0 s)t + π/3.0]

Question 17

A 5.0-kg block is attached to an ideal massless spring whose spring constant is 125 N/m. The block is pulled from its equilibrium position at x = 0.00 m to a position at x = +0.687 m and is released from rest. The block then executes lightly damped oscillation along the x-axis, and the damping force is proportional to the velocity. When the block first returns to x = 0.00 m, its x component of velocity is -2.0 m/s and its x component of acceleration is +5.6 m/s2.
(a) What is the magnitude of the acceleration of the block upon release at x = +0.687 m.
(b) Find the damping constant b.

Accepted Answer

(a) 17.2 m

Question 18

An object of mass 6.8 kg is attached to an ideal massless spring of spring constant 1690 N/m. The object is Calculate the maximum speed the object reaches during its motion.

Accepted Answer

The answer of An object of mass 6.8 kg is...

Question 19

A 56 kg bungee jumper jumps off a bridge and undergoes simple harmonic motion. If the period of oscillation is 11.2 s, what is the spring constant of the bungee cord, assuming it has negligible mass compared to that of the jumper?

Accepted Answer

A)  17.6 N/m 
B)  21.1 N/m 
C)  28.2 N/m 
A)  17.6 N/m 
B)  21.1 N/m 
C)  28.2 N/m

Question 20

An ideal massless spring with a spring constant of 2.00 N/m is attached to an object of 75.0 g. The system has a small amount of damping. If the amplitude of the oscillations decreases from 10.0 mm to 5.00 mm in 15.0 s, what is the magnitude of the damping constant b?

Accepted Answer

A)  0.00693 kg/s 
B)  0.0462 kg/s 
C)  0.00762 kg/s 
D)  0.0100 kg/s 
E)  0.00857 kg/s 
A)  0.00693 kg/s 
B)  0.0462 kg/s 
C)  0.00762 kg/s 
D)  0.0100 kg/s 
E)  0.00857 kg/s

Exam 14: Oscillations

A mass M is attached to an ideal massless spring. When this system is set in motion, it has a period T. What is the period if the mass is doubled to 2M?

In designing buildings to be erected in an area prone to earthquakes, what relationship should the designer try to achieve between the natural frequency of the building and the typical earthquake frequencies?

A frictionless pendulum released from 65 degrees with the vertical will vibrate with the same frequency as if it were released from 5 degrees with the vertical because the period is independent of the amplitude and mass.

A frictionless simple pendulum on Earth has a period of 1.75 s. On Planet X its period is 2.14 s. What is the acceleration due to gravity on Planet X?

If we double only the amplitude of a vibrating ideal mass-and-spring system, the mechanical energy of the system

An object of mass 8.0 kg is attached to an ideal massless spring and allowed to hang in the Earth's gravitational field. The spring stretches 3.6 cm before it reaches its equilibrium position. If this system is allowed to oscillate, what will be its frequency?

The amplitude of a lightly damped harmonic oscillator decreases from 60.0 cm to 40.0 cm in 10.0 s. What will be the amplitude of the harmonic oscillator after another 10.0 s passes?

An object is attached to a vertical ideal massless spring and bobs up and down between the two extreme points A and B. When the kinetic energy of the object is a minimum, the object is located

A 2.15 kg lightly damped harmonic oscillator has an angular oscillation frequency of 0.261 rad/s. If the maximum displacement of 2.0 m occurs when t = 0.00 s, and the damping constant b is 0.74 kg/s what is the object's displacement when t = 4.01 s?

The x component of the velocity of an object vibrating along the x-axis obeys the equation vx(t) = (0.445 m/s) sin[(25.4 rad/s)t + 0.223]. (a) What is the amplitude of the motion of this object? (b) What is the maximum acceleration of the vibrating object?

A sewing machine needle moves up and down in simple harmonic motion with an amplitude of 1.27 cm and a frequency of 2.55 Hz. (a) What is the maximum speed of the needle? (b) What is the maximum acceleration of the needle?

The simple harmonic motion of an object is described by the graph shown in the figure. What is the equation for the position x(t) of the object as a function of time t?

An object of mass 6.8 kg is attached to an ideal massless spring of spring constant 1690 N/m. The object is Calculate the maximum speed the object reaches during its motion.

A 56 kg bungee jumper jumps off a bridge and undergoes simple harmonic motion. If the period of oscillation is 11.2 s, what is the spring constant of the bungee cord, assuming it has negligible mass compared to that of the jumper?

An ideal massless spring with a spring constant of 2.00 N/m is attached to an object of 75.0 g. The system has a small amount of damping. If the amplitude of the oscillations decreases from 10.0 mm to 5.00 mm in 15.0 s, what is the magnitude of the damping constant b?

Concepts of Motion

Kinematics in One Dimension

Vectors and Coordinate Systems

Kinematics in Two Dimensions

Force and Motion

Dynamics I: Motion Along a Line

Newtons Third Law

Dynamics Ii: Motion in a Plane

Impulse and Momentum

Energy

Work

Rotation of a Rigid Body

Newtons Theory of Gravity

Fluids and Elasticity

A Macroscopic Description of Matter

Work, Heat, and the First Law of Thermodynamics

The Micromacro Connection

Heat Engines and Refrigerators

Traveling Waves

Superpositions

Wave Optics

Ray Optics

Optical Instruments

Electric Charges and Forces

The Electric Field

Gausss Law

The Electric Potential

Potential and Field

Current and Resistance

Fundamentals of Circuits

The Magnetic Field

Electromagnetic Induction

Electromagnetic Fields and Waves

Ac Circuits

Relativity

The Foundations of Modern Physics

Quantization

Wave Functions and Uncertainty

One-Dimensional Quantum Mechanics

Atomic Physics

Nuclear Physics

Filters

The x component of the velocity of an object vibrating along the x-axis obeys the equation v_x(t) = (0.445 m/s) sin[(25.4 rad/s)t + 0.223]. (a) What is the amplitude of the motion of this object? (b) What is the maximum acceleration of the vibrating object?