Question 1

To double the total energy of a mass oscillating at the end of a spring with amplitude A,we need to

Accepted Answer

A) increase the angular frequency by   . 
B) increase the amplitude by   . 
C) increase the amplitude by 2. 
D) increase the angular frequency by 2. 
E) increase the amplitude by 4 and decrease the angular frequency by   . 
A) increase the angular frequency by   . 
B) increase the amplitude by   . 
C) increase the amplitude by 2. 
D) increase the angular frequency by 2. 
E) increase the amplitude by 4 and decrease the angular frequency by   .

Question 2

Simple harmonic oscillations can be modeled by the projection of circular motion at constant angular velocity onto a diameter of the circle.When this is done,the analog along the diameter of the acceleration of the particle executing simple harmonic motion is

Accepted Answer

A) the displacement from the center of the diameter of the projection of the position of the particle on the circle. 
B) the projection along the diameter of the velocity of the particle on the circle. 
C) the projection along the diameter of tangential acceleration of the particle on the circle. 
D) the projection along the diameter of centripetal acceleration of the particle on the circle. 
E) meaningful only when the particle moving in the circle also has a non-zero tangential acceleration. 
A) the displacement from the center of the diameter of the projection of the position of the particle on the circle. 
B) the projection along the diameter of the velocity of the particle on the circle. 
C) the projection along the diameter of tangential acceleration of the particle on the circle. 
D) the projection along the diameter of centripetal acceleration of the particle on the circle. 
E) meaningful only when the particle moving in the circle also has a non-zero tangential acceleration.

Question 3

An archer pulls her bow string back 0.40 m by exerting a force that increases uniformly from zero to 240 N.What is the equivalent spring constant of the bow,and how much work is done in pulling the bow?

Accepted Answer

The answer of An archer pulls her bow string back...

Question 4

A mass m = 2.0 kg is attached to a spring having a force constant k = 290 N/m as in the figure.The mass is displaced from its equilibrium position and released.Its frequency of oscillation (in Hz)is approximately

Accepted Answer

A) 12 
B) 0.50 
C) 0.010 
D) 1.9 
E) 0.080 
A) 12 
B) 0.50 
C) 0.010 
D) 1.9 
E) 0.080

Question 5

An object of mass m is attached to string of length L.When it is released from point A,the object oscillates between points A and B.Which statement about the system consisting of the pendulum and the Earth is correct?

Accepted Answer

A) The gravitational potential energy of the system is greatest at A and B. 
B) The kinetic energy of mass m is greatest at point O. 
C) The greatest rate of change of momentum occurs at A and B. 
D) All of the above are correct. 
E) Only (a)and (b)above are correct. 
A) The gravitational potential energy of the system is greatest at A and B. 
B) The kinetic energy of mass m is greatest at point O. 
C) The greatest rate of change of momentum occurs at A and B. 
D) All of the above are correct. 
E) Only (a)and (b)above are correct.

Question 6

The oscillation of the 2.0-kg mass on a spring is described by  
Where x is in centimeters and t is in seconds.What is the force constant of the spring?

Accepted Answer

A) 4.0 N/m 
B) 0.80 N/m 
C) 16 N/m 
D) 32 N/m 
E) 2.0   N/m 
A) 4.0 N/m 
B) 0.80 N/m 
C) 16 N/m 
D) 32 N/m 
E) 2.0   N/m

Question 7

A body oscillates with simple harmonic motion along the x axis.Its displacement varies with time according to the equation x = 5 sin (πt + π/3).The phase (in rad)of the motion at t = 2 s is

Accepted Answer

A) 7π/3 
B) π/3 
C) π 
D) 5π/3 
E) 2π 
A) 7π/3 
B) π/3 
C) π 
D) 5π/3 
E) 2π

Question 8

A body oscillates with simple harmonic motion along the x axis.Its displacement varies with time according to the equation x = 5.0 sin (πt + π/3).The velocity (in m/s)of the body at t = 1.0 s is

Accepted Answer

A) +7.9 
B) −7.9 
C) −14 
D) +14 
E) −5.0 
A) +7.9 
B) −7.9 
C) −14 
D) +14 
E) −5.0

Question 9

In the figure below,a disk (radius R = 1.0 m,mass = 2.0 kg)is suspended from a pivot a distance d = 0.25 m above its center of mass.For a circular disk,  
)The angular frequency (in rad/s)for small oscillations is approximately

Accepted Answer

A) 4.2 
B) 2.1 
C) 1.5 
D) 1.0 
E) 3.8 
A) 4.2 
B) 2.1 
C) 1.5 
D) 1.0 
E) 3.8

Question 10

The mat of a trampoline is held by 32 springs,each having a spring constant of 5 000 N/m.A person with a mass of 40.0 kg jumps from a platform 1.93 m high onto the trampoline.Determine the stretch of each of the springs.

Accepted Answer

The answer of The mat of a trampoline is held...

Question 11

A torsional pendulum consists of a solid disk (mass = 2.0 kg,radius = 1.0 m)suspended by a wire attached to a rigid support.The body oscillates about the support wire.If the torsion constant is 16 N⋅m/rad.What is the angular frequency (in rad/s)?

Accepted Answer

A) 2 
B) 4 
C) 6 
D) 8 
E) 7 
A) 2 
B) 4 
C) 6 
D) 8 
E) 7

Question 12

At sea level,at a latitude where  
,a pendulum that takes 2.00 s for a complete swing back and forth has a length of 0.993 m.What is the value of g in m/s2 at a location where the length of such a pendulum is 0.970 m?

Accepted Answer

A) 0.098 3 
B) 3.05 
C) 9.57 
D) 10.0 
E) 38.3 
A) 0.098 3 
B) 3.05 
C) 9.57 
D) 10.0 
E) 38.3

Question 13

Exhibit 15-1
A graph of position versus time for an object oscillating at the free end of a horizontal spring is shown below.A point or points at which the object has positive velocity and zero acceleration is(are)   Use this exhibit to answer the following question(s).
-Refer to Exhibit 15-1.The point at which the object has zero velocity and positive acceleration is

Accepted Answer

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

Question 14

Which of the following combinations of variables results in the greatest period for a pendulum?

Accepted Answer

A) length = L,mass = M,and maximum angular displacement = 3 degrees 
B) length = 2L,mass = M/2,and maximum angular displacement = 1 degree 
C) length = 1.5L,mass = 2M,and maximum angular displacement = 2 degrees 
D) length =   L,mass =   M,and maximum angular displacement =   degrees 
E) length =   L,mass = 4M,and maximum angular displacement = 4 degrees 
A) length = L,mass = M,and maximum angular displacement = 3 degrees 
B) length = 2L,mass = M/2,and maximum angular displacement = 1 degree 
C) length = 1.5L,mass = 2M,and maximum angular displacement = 2 degrees 
D) length =   L,mass =   M,and maximum angular displacement =   degrees 
E) length =   L,mass = 4M,and maximum angular displacement = 4 degrees

Question 15

The figure shows a uniform rod (length L = 1.0 m,mass = 2.0 kg)suspended from a pivot a distance d = 0.25 m above its center of mass.The angular frequency (in rad/s)for small oscillations is approximately

Accepted Answer

A) 1.0 
B) 2.5 
C) 1.5 
D) 4.1 
E) 3.5 
A) 1.0 
B) 2.5 
C) 1.5 
D) 4.1 
E) 3.5

Question 16

An ore car of mass 4 000 kg starts from rest and rolls downhill on tracks from a mine.A spring with k = 400 000 N/m is located at the end of the tracks.At the spring's maximum compression,the car is at an elevation 10 m lower than its elevation at the starting point.How much is the spring compressed in stopping the ore car? Ignore friction.

Accepted Answer

The answer of An ore car of mass 4 000...

Question 17

A weight of mass m is at rest at O when suspended from a spring,as shown.When it is pulled down and released,it oscillates between positions A and B.Which statement about the system consisting of the spring and the mass is correct?

Accepted Answer

A) The gravitational potential energy of the system is greatest at A. 
B) The elastic potential energy of the system is greatest at O. 
C) The rate of change of momentum has its greatest magnitude at A and B. 
D) The rate of change of gravitational potential energy is smallest at O. 
E) The rate of change of gravitational potential energy has its greatest magnitude at A and B. 
A) The gravitational potential energy of the system is greatest at A. 
B) The elastic potential energy of the system is greatest at O. 
C) The rate of change of momentum has its greatest magnitude at A and B. 
D) The rate of change of gravitational potential energy is smallest at O. 
E) The rate of change of gravitational potential energy has its greatest magnitude at A and B.

Question 18

When a damping force is applied to a simple harmonic oscillator which has angular frequency ω0 in the absence of damping,the new angular frequency ω is such that

Accepted Answer

A) ω 0. 
B) ω = ω0. 
C) ω > ω0. 
D) ωT 0T0. 
E) ωT > ω0T0. 
A) ω 0. 
B) ω = ω0. 
C) ω > ω0. 
D) ωT 0T0. 
E) ωT > ω0T0.

Question 19

The mass in the figure below slides on a frictionless surface.When the mass is pulled out,spring 1 is stretched a distance x1 from its equilibrium position and spring 2 is stretched a distance x2.The spring constants are k1 and k2 respectively.The force pulling back on the mass is:

Accepted Answer

A) −k2x1. 
B) −k2x2. 
C) −(k1x1 + k2x2). 
D)    . 
E)    . 
A) −k2x1. 
B) −k2x2. 
C) −(k1x1 + k2x2). 
D)    . 
E)    .

Question 20

In the figure below,a hoop (radius R = 1.0 m,mass = 2.0 kg)having four spokes of negligible mass is suspended from a pivot a distance d = .25 m above its center of mass.The angular frequency (in rad/s)for small oscillations is approximately

Accepted Answer

A) 4.0 
B) 2.5 
C) 1.5 
D) 1.0 
E) 0.5 
A) 4.0 
B) 2.5 
C) 1.5 
D) 1.0 
E) 0.5

Exam 15: Oscillatory Motion

To double the total energy of a mass oscillating at the end of a spring with amplitude A,we need to

Simple harmonic oscillations can be modeled by the projection of circular motion at constant angular velocity onto a diameter of the circle.When this is done,the analog along the diameter of the acceleration of the particle executing simple harmonic motion is

An archer pulls her bow string back 0.40 m by exerting a force that increases uniformly from zero to 240 N.What is the equivalent spring constant of the bow,and how much work is done in pulling the bow?

A mass m = 2.0 kg is attached to a spring having a force constant k = 290 N/m as in the figure.The mass is displaced from its equilibrium position and released.Its frequency of oscillation (in Hz)is approximately

An object of mass m is attached to string of length L.When it is released from point A,the object oscillates between points A and B.Which statement about the system consisting of the pendulum and the Earth is correct?

The oscillation of the 2.0-kg mass on a spring is described by Where x is in centimeters and t is in seconds.What is the force constant of the spring?

A body oscillates with simple harmonic motion along the x axis.Its displacement varies with time according to the equation x = 5 sin (πt + π/3).The phase (in rad)of the motion at t = 2 s is

A body oscillates with simple harmonic motion along the x axis.Its displacement varies with time according to the equation x = 5.0 sin (πt + π/3).The velocity (in m/s)of the body at t = 1.0 s is

In the figure below,a disk (radius R = 1.0 m,mass = 2.0 kg)is suspended from a pivot a distance d = 0.25 m above its center of mass.For a circular disk, )The angular frequency (in rad/s)for small oscillations is approximately

The mat of a trampoline is held by 32 springs,each having a spring constant of 5 000 N/m.A person with a mass of 40.0 kg jumps from a platform 1.93 m high onto the trampoline.Determine the stretch of each of the springs.

A torsional pendulum consists of a solid disk (mass = 2.0 kg,radius = 1.0 m)suspended by a wire attached to a rigid support.The body oscillates about the support wire.If the torsion constant is 16 N⋅m/rad.What is the angular frequency (in rad/s)?

At sea level,at a latitude where ,a pendulum that takes 2.00 s for a complete swing back and forth has a length of 0.993 m.What is the value of g in m/s2 at a location where the length of such a pendulum is 0.970 m?

Which of the following combinations of variables results in the greatest period for a pendulum?

The figure shows a uniform rod (length L = 1.0 m,mass = 2.0 kg)suspended from a pivot a distance d = 0.25 m above its center of mass.The angular frequency (in rad/s)for small oscillations is approximately

A weight of mass m is at rest at O when suspended from a spring,as shown.When it is pulled down and released,it oscillates between positions A and B.Which statement about the system consisting of the spring and the mass is correct?

When a damping force is applied to a simple harmonic oscillator which has angular frequency ω0 in the absence of damping,the new angular frequency ω is such that

The mass in the figure below slides on a frictionless surface.When the mass is pulled out,spring 1 is stretched a distance x1 from its equilibrium position and spring 2 is stretched a distance x2.The spring constants are k1 and k2 respectively.The force pulling back on the mass is:

In the figure below,a hoop (radius R = 1.0 m,mass = 2.0 kg)having four spokes of negligible mass is suspended from a pivot a distance d = .25 m above its center of mass.The angular frequency (in rad/s)for small oscillations is approximately

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At sea level,at a latitude where ,a pendulum that takes 2.00 s for a complete swing back and forth has a length of 0.993 m.What is the value of g in m/s² at a location where the length of such a pendulum is 0.970 m?

When a damping force is applied to a simple harmonic oscillator which has angular frequency ω₀ in the absence of damping,the new angular frequency ω is such that

The mass in the figure below slides on a frictionless surface.When the mass is pulled out,spring 1 is stretched a distance x₁ from its equilibrium position and spring 2 is stretched a distance x₂.The spring constants are k₁ and k₂ respectively.The force pulling back on the mass is: