Question 1

In simple harmonic motion, the acceleration is proportional to

Accepted Answer

A) the velocity. 
B) the frequency. 
C) the amplitude. 
D) the displacement. 
E) all of the above 
A) the velocity. 
B) the frequency. 
C) the amplitude. 
D) the displacement. 
E) all of the above D

Question 2

A pendulum is made by suspending a solid circular disk from a pivot point that is at the edge of the disk with the plane of the disk lying in the vertical plane. The period of oscillation of the disk is T. If a disk with the same radius but a mass four times is great is suspended the same way, what will be its period of oscillation?

Accepted Answer

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

Question 3

A 2.00-kg mass oscillates on the end of a spring with spring constant 12.0 N/m. Its amplitude of oscillation decreases from 10.0 cm to 1.0 cm in 4.00 minutes. What is the linear damping coefficient of this oscillator?

Accepted Answer

A) 134 N∙s/m 
B) 1.76 N∙s/m 
C) 0.311 N∙s/m 
D) 0.0384 N∙s/m 
E) 0.622 N∙s/m 
A) 134 N∙s/m 
B) 1.76 N∙s/m 
C) 0.311 N∙s/m 
D) 0.0384 N∙s/m 
E) 0.622 N∙s/m D

Question 4

The x-component of motion of an object is given by x(t) = Axcos(ωxt + φx) and the y-component of motion of the object is given by y(t) = Aycos(ωyt + φy). What relationships between the A,ω, and φ parameters must be true so that the motion of the object is on a circle?

Accepted Answer

A) Ax = Ay, ωx = ωy, and φx = φy  
B) Ax = ±Ay, ωx = ±ωy  
C) Ax = ±Ay, ωx = ωy, and φx = φy ± π/2 
D) Ax = Ay, ωx = ±ωy, and φx = φy  
E) Ax = ±Ay, ωx = ±ωy, and φx = φy ± π/2 
A) Ax = Ay, ωx = ωy, and φx = φy  
B) Ax = ±Ay, ωx = ±ωy  
C) Ax = ±Ay, ωx = ωy, and φx = φy ± π/2 
D) Ax = Ay, ωx = ±ωy, and φx = φy  
E) Ax = ±Ay, ωx = ±ωy, and φx = φy ± π/2

Question 5

The position of an air-track cart that is oscillating on a spring is given by x = (12.4 cm) cos[(6.35s-1)t]. At what value of t after t = 0 s is the cart first located at x = 8.47 cm?

Accepted Answer

A) 4.34 s 
B) 0.108 s 
C) 0.129 s 
D) 7.39 s 
E) 7.75 s 
A) 4.34 s 
B) 0.108 s 
C) 0.129 s 
D) 7.39 s 
E) 7.75 s

Question 6

Why are troops instructed to break step when they are marching over a bridge?

Accepted Answer

If all the soldiers march in step, a sin

Question 7

The velocity of a mass attached to a spring is given by v = (1.5 cm/s) sin(ωt + π/2), where ω = 3.0 rad/s. What is the corresponding expression for x?

Accepted Answer

A) x = -(4.50 cm) sin(ωt + π/2) 
B) x = (4.50 cm) cos(ωt + π/2) 
C) x = -(0.50 cm) cos(ωt - π/2) 
D) x = -(0.50 cm) cos(ωt + π/2) 
E) x = -(0.50 cm) sin(ωt + π/2) 
A) x = -(4.50 cm) sin(ωt + π/2) 
B) x = (4.50 cm) cos(ωt + π/2) 
C) x = -(0.50 cm) cos(ωt - π/2) 
D) x = -(0.50 cm) cos(ωt + π/2) 
E) x = -(0.50 cm) sin(ωt + π/2)

Question 8

The position of a mass that is oscillating on a spring is given by x = (12.3 cm) cos[(1.26s-1)t]. What is the velocity of the mass when t = 0.815 s?

Accepted Answer

A) - 13.3 cm/s 
B) 13.3 cm/s 
C) 8.02 cm/s 
D) - 8.02 cm/s 
E) 0 cm/s 
A) - 13.3 cm/s 
B) 13.3 cm/s 
C) 8.02 cm/s 
D) - 8.02 cm/s 
E) 0 cm/s

Question 9

A mass of 1.53 kg is attached to a spring and the system is undergoing simple harmonic oscillations with a frequency of 1.95 Hz and an amplitude of 7.50 cm. What is the speed of the mass when it is 3.00 cm from its equilibrium position?

Accepted Answer

A) 0.0368 m/s 
B) 0.551 m/s 
C) 0.421 m/s 
D) 0.842 m/s 
E) 0.919 m/s 
A) 0.0368 m/s 
B) 0.551 m/s 
C) 0.421 m/s 
D) 0.842 m/s 
E) 0.919 m/s

Question 10

The maximum speed of a 3.00-kg object in simple harmonic motion is 4.00 m/s. The maximum acceleration of the object is 5.00 m/s2. What is the period of simple harmonic motion?

Accepted Answer

A) 1.25 s 
B) 0.417 s 
C) 0.800 s 
D) 5.03 s 
E) 3.75 s 
A) 1.25 s 
B) 0.417 s 
C) 0.800 s 
D) 5.03 s 
E) 3.75 s

Question 11

A nail is stuck into the side of a car tire. As the car drives down a level road at constant speed, which of the following is simple harmonic motion?

Accepted Answer

A) the motion of the center of the tire 
B) the vertical component of motion of the nail 
C) the horizontal component of motion of the nail 
D) both answers A and B 
E) none of the above 
A) the motion of the center of the tire 
B) the vertical component of motion of the nail 
C) the horizontal component of motion of the nail 
D) both answers A and B 
E) none of the above

Question 12

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

Accepted Answer

If possible, the natural frequ

Question 13

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

Accepted Answer

-(519 cm/s

Question 14

In 1851 Jean Bernard Leon Foucault demonstrated the rotation of the Earth using a pendulum 11.0 m long, which was set up in the Paris Observatory. What was the period of oscillation of the pendulum?

Accepted Answer

A) 6.65 s 
B) 5.63 s 
C) 1.79 s 
D) 2.12 s 
E) 2.58 s 
A) 6.65 s 
B) 5.63 s 
C) 1.79 s 
D) 2.12 s 
E) 2.58 s

Question 15

A vertical spring has a mass hanging from it, which is displaced from the equilibrium position and begins to oscillate. At what point does the system have the least potential energy?

Accepted Answer

A) at the highest point 
B) at one-fourth of the distance between the highest point and lowest point 
C) at the lowest point 
D) at the point where the spring is unstretched 
E) at the equilibrium point 
A) at the highest point 
B) at one-fourth of the distance between the highest point and lowest point 
C) at the lowest point 
D) at the point where the spring is unstretched 
E) at the equilibrium point

Question 16

Any oscillating system for which the net restoring force is directly proportional to the displacement is said to exhibit simple harmonic motion.

Accepted Answer

A) True 
 B)False

Question 17

Grandfather clocks are designed in a way that the weight at the bottom of the pendulum can be moved up or down by turning a small screw. Suppose you have a grandfather clock at home that runs slow. Should you turn the adjusting screw so as to raise the weight or lower the weight?

Accepted Answer

A) Raise it. 
B) Lower it. 
C) It doesn't matter if you raise or lower the weight as long as you displace it by the right amount. 
D) It doesn't matter if you raise or lower the weight, as long as you displace it with the correct initial velocity. 
E) Raising or lowering the weight doesn't help, the screw is there so that you can add or take away weight. 
A) Raise it. 
B) Lower it. 
C) It doesn't matter if you raise or lower the weight as long as you displace it by the right amount. 
D) It doesn't matter if you raise or lower the weight, as long as you displace it with the correct initial velocity. 
E) Raising or lowering the weight doesn't help, the screw is there so that you can add or take away weight.

Question 18

In a grandfather clock, the pendulum measures the time elapsed. A grandfather clock is gaining time. Should you shorten or lengthen the pendulum?

Accepted Answer

You should lengthen

Question 19

The amplitude of a linearly 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) 16.7 cm 
C) 30.0 cm 
D) 0.00 cm 
E) 26.7 cm 
A) 20.0 cm 
B) 16.7 cm 
C) 30.0 cm 
D) 0.00 cm 
E) 26.7 cm

Question 20

A long thin uniform rod of length 1.50 m is to be suspended from a pivot so that its pendulum motion takes 3.00 s. How far from the center of the rod should the pivot be placed?

Accepted Answer

A) 7.98 cm 
B) 7.52 cm 
C) 8.72 cm 
D) 8.40 cm 
E) 23.4 cm 
A) 7.98 cm 
B) 7.52 cm 
C) 8.72 cm 
D) 8.40 cm 
E) 23.4 cm

Exam 14: Oscillations

In simple harmonic motion, the acceleration is proportional to

A 2.00-kg mass oscillates on the end of a spring with spring constant 12.0 N/m. Its amplitude of oscillation decreases from 10.0 cm to 1.0 cm in 4.00 minutes. What is the linear damping coefficient of this oscillator?

The x-component of motion of an object is given by x(t) = Axcos(ωxt + φx) and the y-component of motion of the object is given by y(t) = Aycos(ωyt + φy). What relationships between the A,ω, and φ parameters must be true so that the motion of the object is on a circle?

The position of an air-track cart that is oscillating on a spring is given by x = (12.4 cm) cos[(6.35s-1)t]. At what value of t after t = 0 s is the cart first located at x = 8.47 cm?

Why are troops instructed to break step when they are marching over a bridge?

The velocity of a mass attached to a spring is given by v = (1.5 cm/s) sin(ωt + π/2), where ω = 3.0 rad/s. What is the corresponding expression for x?

The position of a mass that is oscillating on a spring is given by x = (12.3 cm) cos[(1.26s-1)t]. What is the velocity of the mass when t = 0.815 s?

A mass of 1.53 kg is attached to a spring and the system is undergoing simple harmonic oscillations with a frequency of 1.95 Hz and an amplitude of 7.50 cm. What is the speed of the mass when it is 3.00 cm from its equilibrium position?

The maximum speed of a 3.00-kg object in simple harmonic motion is 4.00 m/s. The maximum acceleration of the object is 5.00 m/s2. What is the period of simple harmonic motion?

A nail is stuck into the side of a car tire. As the car drives down a level road at constant speed, which of the following is simple harmonic motion?

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

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

In 1851 Jean Bernard Leon Foucault demonstrated the rotation of the Earth using a pendulum 11.0 m long, which was set up in the Paris Observatory. What was the period of oscillation of the pendulum?

A vertical spring has a mass hanging from it, which is displaced from the equilibrium position and begins to oscillate. At what point does the system have the least potential energy?

Any oscillating system for which the net restoring force is directly proportional to the displacement is said to exhibit simple harmonic motion.

Grandfather clocks are designed in a way that the weight at the bottom of the pendulum can be moved up or down by turning a small screw. Suppose you have a grandfather clock at home that runs slow. Should you turn the adjusting screw so as to raise the weight or lower the weight?

In a grandfather clock, the pendulum measures the time elapsed. A grandfather clock is gaining time. Should you shorten or lengthen the pendulum?

The amplitude of a linearly 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?

A long thin uniform rod of length 1.50 m is to be suspended from a pivot so that its pendulum motion takes 3.00 s. How far from the center of the rod should the pivot be placed?

Introduction, Measurement, Estimating

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Filters

The x-component of motion of an object is given by x(t) = A_xcos(ω_xt + φ_x) and the y-component of motion of the object is given by y(t) = A_ycos(ω_yt + φ_y). What relationships between the A,ω, and φ parameters must be true so that the motion of the object is on a circle?

The position of an air-track cart that is oscillating on a spring is given by x = (12.4 cm) cos[(6.35s^-1)t]. At what value of t after t = 0 s is the cart first located at x = 8.47 cm?

The position of a mass that is oscillating on a spring is given by x = (12.3 cm) cos[(1.26s^-1)t]. What is the velocity of the mass when t = 0.815 s?

The maximum speed of a 3.00-kg object in simple harmonic motion is 4.00 m/s. The maximum acceleration of the object is 5.00 m/s². What is the period of simple harmonic motion?

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