Chapter 14

A 25 kg object is undergoing lightly damped harmonic oscillations. If the maximum displacement of the object from its equilibrium point drops to 1/3 its original value in 1.8 s, what is the value of the damping constant b?

31 kg/s

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

8.73 cm

A simple pendulum consists of a point mass suspended by a massless, unstretchable string. If the mass is doubled while the length of the string remains the same, the period of the pendulum becomes four times greater. becomes twice as great. becomes greater by a factor of sqrt(2) remains unchanged. decreases.

D

For vibrational motion, what term denotes the maximum displacement from the equilibrium position?

amplitude

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

at either A or B

A small block is attached to an ideal spring and is moving in SHM on a horizontal, frictionless surface. The amplitude of the motion is 0.200 m and the period is 3.19 s. What is the acceleration of the block when x = 0.160 m? Express your answer with the appropriate units. What is the speed of the block when x = 0.160 m? Express your answer with the appropriate units.

ax = -0.621 m/s^2 vx = 0.236 m/s

A 45.0 g hard-boiled egg moves on the end of a spring with force constant 25.0 N/m. Its initial displacement 0.500 m. A damping force Fx=−bvx acts on the egg, and the amplitude of the motion decreases to 0.100 m in a time of 5.00 s.

b = 2.90 * 10^-2 kg/s

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.

false

An object is executing simple harmonic motion. What is true about the acceleration of this object? (There may be more than one correct choice.)

The acceleration is zero when the speed of the object is a maximum.

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

increases by a factor of 4

A mass is attached to a vertical spring. The mass exhibits simple harmonic motion between points A and B. Which of the following statements are true? Check all that apply. The mass is located at either point A or B when its potential energy is at minimum. The mass is located midway between points A and B when its kinetic energy is at maximum. The mass is located midway between points A and B when its potential energy is at maximum. The mass is located at either point A or B when its kinetic energy is at minimum.

The mass is located midway between points A and B when its kinetic energy is at maximum. The mass is located at either point A or B when its kinetic energy is at minimum.

Does the period of a pendulum depend on the amplitude? Yes No

Yes

What term denotes the time for one cycle of a periodic process?

period

A certain frictionless simple pendulum having a length L and mass M swings with period T. If both L and M are doubled, what is the new period?

sqrt(2T)

A machine part is undergoing SHM with a frequency of 5.00 Hz and amplitude 1.80 cm. How long does it take the part to go from x = 0 to x = -1.80 cm? Express your answer with the appropriate units.

t = 5.00 * 10^-2 s

In simple harmonic motion, the speed is greatest at that point in the cycle when

the magnitude of the acceleration is a minimum.

An object of mass of 2.0 kg hangs from an ideal massless spring with a spring constant of 50 N/m. An oscillating force F=(4.8⁢N)⁢cos⁡[(3.0⁢rads)⁢t] is applied to the object. What is the amplitude of the resulting oscillations? You can neglect damping.

0.15 m

A 0.025-kg block on a horizontal frictionless surface is attached to an ideal massless spring whose spring constant is 150 N/m. The block is pulled from its equilibrium position at x=0.00m to a displacement x=+0.080m and is released from rest. The block then executes simple harmonic motion along the horizontal x-axis. When the displacement is x=0.024⁢m, what is the kinetic energy of the block?

0.44 J

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?

17.6 N/m

One technique for making images of surfaces at the nanometer scale, including membranes and biomolecules, is dynamic atomic force microscopy. In this technique, a small tip is attached to a cantilever, which is a flexible, rectangular slab supported at one end, like a diving board. The cantilever vibrates, so the tip moves up and down in simple harmonic motion. In one operating mode, the resonant frequency for a cantilever with force constant k = 1000 N/m is 100 kHz. As the oscillating tip is brought within a few nanometers of the surface of a sample (as shown in (Figure 1)), it experiences an attractive force from the surface. For an oscillation with a small amplitude (typically, 0.050 nm), the force F that the sample surface exerts on the tip varies linearly with the displacement x of the tip, |F|=ksurfx, where ksurf is the effective force constant for this force. The net force on the tip is therefore (k+ksurf)x, and the frequency of the oscillation changes slightly due to the interaction with the surface. Measurements of the frequency as the tip moves over different parts of the sample's surface can provide information about the sample. If we model the vibrating system as a mass on a spring, what is the mass necessary to achieve the desired resonant frequency when the tip is not interacting with the surface?

2.5 mg

An object that weighs 2.450 N is attached to an ideal massless spring and undergoes simple harmonic oscillations with a period of 0.640 s. What is the spring constant of the spring?

24.1 N/m

A lightly damped harmonic oscillator, with a damping force proportional to its speed, is oscillating with an amplitude of 0.500 cm at time t=0. When t=8.20⁢s, the amplitude has died down to 0.400 cm. At what value of t will the oscillations have an amplitude of 0.250 cm?

25.5 s

A 0.25 kg ideal harmonic oscillator has a total mechanical energy of 4.0 J. If the oscillation amplitude is 20.0 cm, what is the oscillation frequency?

4.5 Hz

This is an ax - t graph for an object in simple harmonic motion. At which of the following times does the object have the most negative velocity vx ? t=0.10 s t=0.15 s t=0.20 s t=0.25 s Two of the above are tied for most negative velocity

A

This is an x - t graph for an object in simple harmonic motion. At which of the following times does the object have the most negative velocity vx ? t=T/4 t=T/2 t=3T/4 t=T Two of the above are tied for most negative velocity

A

This is the position graph of a mass oscillating on a horizontal spring. What is the phase constant ϕ0? −π/2 rad 0 rad π/2 rad π rad None of these.

A

An object with mass 0.200 kg is acted on by an elastic restoring force with force constant 11.0 N/m. The object is set into oscillation with an initial potential energy of 0.140 J and an initial kinetic energy of 5.30×10−2 J. What is the amplitude of oscillation? Express your answer with the appropriate units. What is the potential energy when the displacement is one-half the amplitude? Express your answer with the appropriate units. At what displacement are the kinetic and potential energies equal? Express your answer with the appropriate units. What is the value of the phase angle ϕ if the initial velocity is positive and the initial displacement is negative? Express your answer in radians.

A = 0.187 m U = 4.83 * 10^-2 J x = 0.132 theta = -2.59 rad

A 2.00 kg, frictionless block is attached to an ideal spring with force constant 300 N/m. At t = 0 the block has velocity -4.00 m/s and displacement +0.200 m away from equilibrium. Find the amplitude. Express your answer to three significant figures and include the appropriate units. Find the phase angle. Express your answer in radians. Choose an equation for the position as a function of time.

A = 0.383 m theta = 1.02 rad x(t) = 0.383 * cos(12.2t + 1.02)

Which of the following statements are true? Check all that apply. The increase in amplitude of an oscillation by a driving force is called forced oscillation. An oscillation that is maintained by a driving force is called forced oscillation. The decrease in the amplitude of an oscillation caused by dissipative forces is called damping. In a mechanical system, the amplitude of an oscillation diminishes with time unless the lost mechanical energy is replaced.

An oscillation that is maintained by a driving force is called forced oscillation. The decrease in the amplitude of an oscillation caused by dissipative forces is called damping. In a mechanical system, the amplitude of an oscillation diminishes with time unless the lost mechanical energy is replaced.

A mass on the end of a spring undergoes simple harmonic motion. At the instant when the mass is at its equilibrium position, what is its instantaneous acceleration?

At equilibrium, its instantaneous acceleration is zero.

A mass on the end of a spring undergoes simple harmonic motion. At the instant when the mass is at its equilibrium position, what is its instantaneous velocity?

At equilibrium, its instantaneous velocity is at maximum.

A mass on the end of a spring undergoes simple harmonic motion. At the instant when the mass is at its maximum displacement from equilibrium, what is its instantaneous acceleration?

At maximum displacement, its instantaneous acceleration is also at maximum.

A mass on the end of a spring undergoes simple harmonic motion. At the instant when the mass is at its maximum displacement from equilibrium, what is its instantaneous velocity?

At maximum displacement, its instantaneous velocity is zero.

An object on the end of a spring is oscillating in simple harmonic motion. If the amplitude of oscillation is doubled, how does this affect the oscillation period T and the object's maximum speed vmax ? T and vmax both double T remains the same and vmax doubles T and vmax both remain the same T doubles and vmax remains the same T remains the same and vmax increases by a factor of sqrt(2)

B

This is an ax - t graph for an object in simple harmonic motion. At which of the following times does the object have the most negative displacement x ? t=0.10 s t=0.15 s t=0.20 s t=0.25 s Two of the above are tied for most negative displacement

B

This is an x - t graph for an object in simple harmonic motion. At which of the following times is the kinetic energy of the object the greatest? t=T/8 t=T/4 t=3T/8 t=T/2 Two of the above are tied for greatest potential energy

B

A block oscillates on a very long horizontal spring. The graph shows the block's kinetic energy as a function of position. What is the spring constant? 1 N/m 2 N/m 4 N/m 8 N/m I have no idea

C

The figure shows four oscillators at t=0 . For which is the phase constant ϕ0=−π/4 ? A B C D

C

This is an x - t graph for an object in simple harmonic motion. At which of the following times does the object have the most negative acceleration ax ? t=T/4 t=T/2 t=3T/4 t=T Two of the above are tied for most negative acceleration

D

This is an x - t graph for an object in simple harmonic motion. At which of the following times is the potential energy of the spring the greatest? t=T/8 t=T/4 t=3T/8 t=T/2 Two of the above are tied for greatest potential energy

D

This is the position graph of a mass oscillating on a horizontal spring. What is the phase constant ϕ0 ? −π/2 rad 0 rad π/2 rad π rad None of these

D

A restoring force of magnitude F acts on a system with a displacement of magnitude x. In which of the following cases will the system undergo simple harmonic motion?

F (inf. sign) x

A certain alarm clock ticks four times each second, with each tick representing half a period. The balance wheel consists of a thin rim with radius 0.56 cm, connected to the balance staff by thin spokes of negligible mass. The total mass of the balance wheel is 1.0 g. What is the moment of inertia of the balance wheel about its shaft? Express your answer with the appropriate units. What is the torsion constant of the hairspring? Express your answer in N⋅m/rad.

I = 3.1 * 10^-8 kg*m^2 K = 5.0 * 10^-6 N*m/rad

A 1.80 kg monkey wrench is pivoted 0.250 m from its center of mass and allowed to swing as a physical pendulum. The period for small-angle oscillations is 0.940 s. What is the moment of inertia of the wrench about an axis through the pivot? Express your answer with the appropriate units. If the wrench is initially displaced 0.400 rad from its equilibrium position, what is the angular speed of the wrench as it passes through the equilibrium position? Express your answer in radians per second.

I = 9.87 * 10^-2 kg*m^2 max = 2.66 rad/s

A large, 42.0 kg bell is hung from a wooden beam so it can swing back and forth with negligible friction. The bell's center of mass is 0.80 m below the pivot. The bell's moment of inertia about an axis at the pivot is 18.0 kg⋅m2. The clapper is a small, 1.8 kg mass attached to one end of a slender rod that has length L and negligible mass. The other end of the rod is attached to the inside of the bell; the rod can swing freely about the same axis as the bell. What should be the length L of the clapper rod for the bell to ring silently - that is, for the period of oscillation for the bell to equal that for the clapper? Express your answer with the appropriate units.

L = 0.54 m

Which of the following statements are true? Check all that apply. All periodic motions are simple harmonic motions. A system that undergoes periodic motion never has a stable equilibrium position. Simple harmonic motion is periodic motion under the action of a restoring force that is directly proportional to the displacement from equilibrium. Simple harmonic motion is periodic motion under the action of a restoring force that is inversely proportional to the displacement from equilibrium. A system that undergoes periodic motion always has a stable equilibrium position.

Simple harmonic motion is periodic motion under the action of a restoring force that is directly proportional to the displacement from equilibrium. A system that undergoes periodic motion always has a stable equilibrium position.

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

T

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?

The natural frequency of the building should be very different from typical earthquake frequencies.

A simple pendulum consists of a point mass suspended by a weightless, rigid wire in a uniform gravitation field. Which of the following statements are true when the system undergoes small oscillations? Check all that apply. The period is independent of the length of the wire. The period is proportional to the square root of the length of the wire. The period is independent of the suspended mass. The period is inversely proportional to the suspended mass. The period is inversely proportional to the length of the wire. The period is proportional to the suspended mass.

The period is proportional to the square root of the length of the wire. The period is independent of the suspended mass.

A certain simple pendulum has a period on the earth of 1.50 s. What is its period on the surface of Mars, where g = 3.71 m/s2? Express your answer with the appropriate units.

Tm = 2.4 s