Question 1

The mass in the figure slides on a frictionless surface.If m = 2 kg,k1 = 800 N/m and k2 = 500 N/m,the frequency of oscillation (in Hz)is approximately

Accepted Answer

A) 6 
B) 2 
C) 4 
D) 8 
E) 10 
A) 6 
B) 2 
C) 4 
D) 8 
E) 10

Question 2

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 3

A uniform rod (mass m = 1.0 kg and length L = 2.0 m)pivoted at one end oscillates in a vertical plane as shown below.The period of oscillation (in s)is approximately

Accepted Answer

A) 4.0 
B) 1.6 
C) 3.2 
D) 2.3 
E) 2.0 
A) 4.0 
B) 1.6 
C) 3.2 
D) 2.3 
E) 2.0

Question 4

For the wave described by y = 0.02 sin (kx)at t = 0 s,the first maximum at a positive x coordinate occurs where x = 4 m.Where on the positive x axis does the second maximum occur?

Accepted Answer

A) 20 m 
B) 18 m 
C) 24 m 
D) 28 m 
E) 16 m 
A) 20 m 
B) 18 m 
C) 24 m 
D) 28 m 
E) 16 m

Question 5

Two circus clowns (each having a mass of 50 kg)swing on two flying trapezes (negligible mass,length 25 m)shown in the figure.At the peak of the swing,one grabs the other,and the two swing back to one platform.The time for the forward and return motion is

Accepted Answer

A) 10 s 
B) 50 s 
C) 15 s 
D) 20 s 
E) 25 s 
A) 10 s 
B) 50 s 
C) 15 s 
D) 20 s 
E) 25 s

Question 6

A horizontal plank (m = 2.0 kg,L = 1.0 m)is pivoted at one end.A spring (k = 1.0* 103 N/m)is attached at the other end,as shown in the figure.Find the angular frequency (in rad/s)for small oscillations.

Accepted Answer

A) 39 
B) 44 
C) 55 
D) 66 
E) 25 
A) 39 
B) 44 
C) 55 
D) 66 
E) 25

Question 7

Three pendulums with strings of the same length and bobs of the same mass are pulled out to angles $\theta$1,$\theta$2 and $\theta$3 respectively and released.The approximation sin $\theta$ = $\theta$ holds for all three angles,with $\theta$3 > $\theta$2 > $\theta$1.How do the angular frequencies of the three pendulums compare?

Accepted Answer

A)  $ \omega $3 >  $ \omega $2 >  $ \omega $1 
B) Need to know amplitudes to answer this question. 
C) Need to know $\sqrt { g / L }$ to answer this question. 
D)  $ \omega $1 >  $ \omega $2 >  $ \omega $3 
E)  $ \omega $1 =  $ \omega $2 =  $ \omega $3 
A)  $ \omega $3 >  $ \omega $2 >  $ \omega $1 
B) Need to know amplitudes to answer this question. 
C) Need to know $\sqrt { g / L }$ to answer this question. 
D)  $ \omega $1 >  $ \omega $2 >  $ \omega $3 
E)  $ \omega $1 =  $ \omega $2 =  $ \omega $3

Question 8

When a damping force is applied to a simple harmonic oscillator which has angular frequency  $ \omega $0 in the absence of damping,the new angular frequency  $ \omega $ is such that

Accepted Answer

A)  $ \omega $ 0. 
B)  $ \omega $ =  $ \omega $0. 
C)  $ \omega $>  $ \omega $0. 
D)  $ \omega $T 0T0. 
E)  $ \omega $T >  $ \omega $0T0. 
A)  $ \omega $ 0. 
B)  $ \omega $ =  $ \omega $0. 
C)  $ \omega $>  $ \omega $0. 
D)  $ \omega $T 0T0. 
E)  $ \omega $T >  $ \omega $0T0.

Question 9

The equation $y = A \sin \left( k x - ? t + \frac { \pi } { 2 } \right)$ is the same as

Accepted Answer

A)  $y = - A \sin \left( k x - \omega t + \frac { \pi } { 2 } \right)$ 
B)  $y = A \cos ( k x - ? t )$ 
C)  $y = - A \cos ( k x - \omega t )$ 
D)  $y = - A \sin \left( k x - \omega t - \frac { \pi } { 2 } \right)$ 
E)  $y = A \sin \left( k x - \omega t + \frac { 3 \pi } { 2 } \right)$ 
A)  $y = - A \sin \left( k x - \omega t + \frac { \pi } { 2 } \right)$ 
B)  $y = A \cos ( k x - ? t )$ 
C)  $y = - A \cos ( k x - \omega t )$ 
D)  $y = - A \sin \left( k x - \omega t - \frac { \pi } { 2 } \right)$ 
E)  $y = A \sin \left( k x - \omega t + \frac { 3 \pi } { 2 } \right)$

Question 10

A 2.00 m-long 6.00 kg ladder pivoted at the top hangs down from a platform at the circus.A 42.0 kg trapeze artist climbs to a point where her center of mass is at the center of the ladder and swings at the system's natural frequency.The angular frequency (in s - 1)of the system of ladder and woman is

Accepted Answer

A) 1.01. 
B) 3.07. 
C) 4.03. 
D) 8.05. 
E) 16.2. 
A) 1.01. 
B) 3.07. 
C) 4.03. 
D) 8.05. 
E) 16.2.

Question 11

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.
-Refer to Exhibit 15-1.The point at which the object has zero velocity and negative 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 12

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 13

If y = 0.02 sin (30x - 400t)(SI units),the angular frequency of the wave is

Accepted Answer

A) 30 rad/s 
B) 30/2 $\pi$ rad/s 
C) 400/2 $\pi$ rad/s 
D) 400 rad/s 
E) 40/3 rad/s 
A) 30 rad/s 
B) 30/2 $\pi$ rad/s 
C) 400/2 $\pi$ rad/s 
D) 400 rad/s 
E) 40/3 rad/s

Question 14

A body of mass 5.0 kg is suspended by a spring which stretches 10 cm when the mass is attached.It is then displaced downward an additional 5.0 cm and released.Its position as a function of time is approximately

Accepted Answer

A) y = -0.10 sin 9.9t 
B) y = 0.10 cos 9.9t 
C) y = -0.10 cos (9.9t + .1) 
D) y = 0.10 sin (9.9t + 5) 
E) y = -0.05 cos 9.9t 
A) y = -0.10 sin 9.9t 
B) y = 0.10 cos 9.9t 
C) y = -0.10 cos (9.9t + .1) 
D) y = 0.10 sin (9.9t + 5) 
E) y = -0.05 cos 9.9t

Question 15

When a damping force is applied to a simple harmonic oscillator which has period T0 in the absence of damping,the new period T is such that

Accepted Answer

A) T 0. 
B) T = T0. 
C) T > T0. 
D)  $ \omega $T 0T0. 
E)  $ \omega $T >  $ \omega $0T0. 
A) T 0. 
B) T = T0. 
C) T > T0. 
D)  $ \omega $T 0T0. 
E)  $ \omega $T >  $ \omega $0T0.

Question 16

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, $I _ { \mathrm { cm } } = \frac { 1 } { 2 } m R ^ { 2 }$ .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 17

The oscillation of the 2.0-kg mass on a spring is described by $x = 3.0 \cos ( 4.0 t + 0.80 )$ 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 $\pi$ N/m 
A) 4.0 N/m 
B) 0.80 N/m 
C) 16 N/m 
D) 32 N/m 
E) 2.0 $\pi$ N/m

Question 18

Write the equation of a wave,traveling along the +x axis with an amplitude of 0.02 m,a frequency of 440 Hz,and a speed of 330 m/sec.

Accepted Answer

A) y = 0.02 sin [880 $\pi$(x/330 - t)] 
B) y = 0.02 cos [880 $\pi$ x/330 -440t] 
C) y = 0.02 sin [880 $\pi$(x/330 + t)] 
D) y = 0.02 sin [2 $\pi$(x/330 + 440t)] 
E) y = 0.02 cos [2 $\pi$(x/330 + 440t)] 
A) y = 0.02 sin [880 $\pi$(x/330 - t)] 
B) y = 0.02 cos [880 $\pi$ x/330 -440t] 
C) y = 0.02 sin [880 $\pi$(x/330 + t)] 
D) y = 0.02 sin [2 $\pi$(x/330 + 440t)] 
E) y = 0.02 cos [2 $\pi$(x/330 + 440t)]

Question 19

If y = 0.02 sin (30x - 400t)(SI units),the frequency of the wave is

Accepted Answer

A) 30 Hz 
B) 15/ $\pi$ Hz 
C) 200/ $\pi$ Hz 
D) 400 Hz 
E) 800 $\pi$Hz 
A) 30 Hz 
B) 15/ $\pi$ Hz 
C) 200/ $\pi$ Hz 
D) 400 Hz 
E) 800 $\pi$Hz

Question 20

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 $\sqrt { 2 }$ . 
B) increase the amplitude by $\sqrt { 2 }$ . 
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 $\frac { 1 } { \sqrt { 2 } }$ . 
A) increase the angular frequency by $\sqrt { 2 }$ . 
B) increase the amplitude by $\sqrt { 2 }$ . 
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 $\frac { 1 } { \sqrt { 2 } }$ .

Exam 12: Oscillatory Motion

The mass in the figure slides on a frictionless surface.If m = 2 kg,k1 = 800 N/m and k2 = 500 N/m,the frequency of oscillation (in Hz)is approximately

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

A uniform rod (mass m = 1.0 kg and length L = 2.0 m)pivoted at one end oscillates in a vertical plane as shown below.The period of oscillation (in s)is approximately

For the wave described by y = 0.02 sin (kx)at t = 0 s,the first maximum at a positive x coordinate occurs where x = 4 m.Where on the positive x axis does the second maximum occur?

Two circus clowns (each having a mass of 50 kg)swing on two flying trapezes (negligible mass,length 25 m)shown in the figure.At the peak of the swing,one grabs the other,and the two swing back to one platform.The time for the forward and return motion is

A horizontal plank (m = 2.0 kg,L = 1.0 m)is pivoted at one end.A spring (k = 1.0* 103 N/m)is attached at the other end,as shown in the figure.Find the angular frequency (in rad/s)for small oscillations.

When a damping force is applied to a simple harmonic oscillator which has angular frequency ω \omega ω 0 in the absence of damping,the new angular frequency ω \omega ω is such that

The equation y=Asin⁡(kx−?t+π2)y = A \sin \left( k x - ? t + \frac { \pi } { 2 } \right)y=Asin(kx−?t+2π​) is the same as

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

If y = 0.02 sin (30x - 400t)(SI units),the angular frequency of the wave is

A body of mass 5.0 kg is suspended by a spring which stretches 10 cm when the mass is attached.It is then displaced downward an additional 5.0 cm and released.Its position as a function of time is approximately

When a damping force is applied to a simple harmonic oscillator which has period T0 in the absence of damping,the new period T is such that

The oscillation of the 2.0-kg mass on a spring is described by x=3.0cos⁡(4.0t+0.80)x = 3.0 \cos ( 4.0 t + 0.80 )x=3.0cos(4.0t+0.80) where x is in centimeters and t is in seconds.What is the force constant of the spring?

Write the equation of a wave,traveling along the +x axis with an amplitude of 0.02 m,a frequency of 440 Hz,and a speed of 330 m/sec.

If y = 0.02 sin (30x - 400t)(SI units),the frequency of the wave is

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

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The mass in the figure slides on a frictionless surface.If m = 2 kg,k₁ = 800 N/m and k₂ = 500 N/m,the frequency of oscillation (in Hz)is approximately

A horizontal plank (m = 2.0 kg,L = 1.0 m)is pivoted at one end.A spring (k = 1.0* 10³ N/m)is attached at the other end,as shown in the figure.Find the angular frequency (in rad/s)for small oscillations.

When a damping force is applied to a simple harmonic oscillator which has angular frequency $\omega$ ₀ in the absence of damping,the new angular frequency $\omega$ is such that

The equation $y = A \sin \left( k x - ? t + \frac { \pi } { 2 } \right)$ is the same as

When a damping force is applied to a simple harmonic oscillator which has period T₀ in the absence of damping,the new period T is such that

The oscillation of the 2.0-kg mass on a spring is described by $x = 3.0 \cos ( 4.0 t + 0.80 )$ where x is in centimeters and t is in seconds.What is the force constant of the spring?