E) x(t) = (4.0 m)cos[(2π/8.0 s)t – π/3.0]

The simple harmonic motion of an object is shown in Fig. 14-1. What is the position of the object as a function of time?

9

By what factor should the length of a simple pendulum be changed in order to triple the period of vibration?

an underdamped situation

Curve A in Fig. 11-1 represents

the magnitude of the acceleration is a minimum.

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

3

Tripling the displacement from equilibrium of an object in simple harmonic motion will change the magnitude of the object’s maximum acceleration by what factor?

The system will resonate and unless some energy is lost the amplitude of the vibrations will increase until the system breaks.

What happens when a periodic driving force is applied at a frequency close to the natural frequency of the system?

produces no change

Doubling only the mass of a vibrating mass-and-spring system produces what effect on the system’s mechanical energy?

0.5f

A mass m hanging on a spring has a natural frequency f. If the mass is increased to 4m, what is the new natural frequency?

constant

The total mechanical energy of a simple harmonic oscillator is

y = (0.01 m) cos (22.1 t)

A 0.30-kg mass is suspended on a spring. In equilibrium the mass stretches the spring 2.0 cm downward. The mass is then pulled an additional distance of 1.0 cm down and released from rest. Write down its equation of motion.

all of these

Which of the following are characteristics of a mass in simple harmonic motion?

I. The motion repeats at regular intervals.

II. The motion is sinusoidal.

III. The restoring force is proportional to the displacement from equilibrium

I. The motion repeats at regular intervals.

II. The motion is sinusoidal.

III. The restoring force is proportional to the displacement from equilibrium

is a maximum

A mass on a spring undergoes SHM. When the mass is at maximum displacement from equilibrium, its instantaneous acceleration

a ball bouncing on the floor

Which of the following is not an example of approximate simple harmonic motion?

the restoring force

Which of the following features of a given pendulum changes when the pendulum is moved from Earth’s surface to the moon?

velocity reaches a maximum

A mass attached to a spring vibrates back and forth. At the equilibrium position, the

x = -(0.50 cm) cos(ωt + π/2)

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?

decrease

If you take a given pendulum to the Moon, where the acceleration of gravity is less than on Earth, the resonant frequency of the pendulum will

A

The graph below is a plot of displacement versus time of a mass oscillating on a spring.

At which point on the graph is the net force on the mass at a maximum?

At which point on the graph is the net force on the mass at a maximum?

The system will resonate and unless some energy is lost the amplitude of the vibrations will increase until the system breaks.

What happens when a periodic driving force is applied at a frequency close to the natural frequency of the system?

A

The graph below is a plot of displacement versus time of a mass oscillating on a spring.

At which point on the graph is the velocity of the mass zero?

At which point on the graph is the velocity of the mass zero?

C

The graph below is a plot of displacement versus time of a mass oscillating on a spring.

At which point on the graph is the acceleration of the mass zero?

At which point on the graph is the acceleration of the mass zero?

increases the energy by a factor of two

Doubling only the spring constant of a vibrating mass-and-spring system produces what effect on the system’s mechanical energy?

sqrt2 t

A mass M is attached to a spring with spring constant k. When this system is set in motion with amplitude A, it has a period T. What is the period if the mass is doubled to 2M?

the potential energy of the spring

The work done to move a spring away from its equilibrium position is equal to

they are inversely related

How are frequency and period related in simple harmonic motion?

increases the energy by a factor of four

Doubling only the amplitude of a vibrating mass-and-spring system produces what effect on the system’s mechanical energy?

an overdamped situation

Curve C in Fig. 11-1 represents

the magnitude of the acceleration is a minimum.

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

at either A or B

A mass is attached to a vertical spring and bobs up and down between points A and B. Where is the mass located when its kinetic energy is a minimum?

the acceleration reaches a maximum.

A simple pendulum swings in simple harmonic motion. At maximum displacement,

amplitude

For a mass hanging from a spring, the maximum displacement the spring is stretched or compressed from its equilibrium position is the system’s

period

For a system in simple harmonic motion, which of the following is the time required to complete a cycle of motion?

0.50s

A mass on a spring undergoes SHM. It goes through 10 complete oscillations in 5.0 s. What is the period?

0.56J

A 0.50-kg mass is attached to a 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. What is the total energy of the system?

acceleration reach a maximum

A mass attached to a spring vibrates back and forth. At maximum displacement, the spring force and the

294 N/m

What is the spring constant of a spring that stretches 2.00 cm when a mass of 0.600 kg is suspended from it?

T

A mass M is attached to a spring with spring constant k. 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?

displacement

Vibration of an object about an equilibrium point is called simple harmonic motion when the restoring force is proportional to

the displacement

In simple harmonic motion, the acceleration is proportional to

at the equilibrium point

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?

midway between A and B

A mass is attached to a vertical spring and bobs up and down between points A and B. Where is the mass located when its kinetic energy is a maximum?

increases the energy by a factor of four

Doubling only the amplitude of a vibrating mass-and-spring system produces what effect on the system’s mechanical energy?

at either A or B

A mass is attached to a vertical spring and bobs up and down between points A and B. Where is the mass located when its potential energy is a maximum?

critical damping

Curve B in Fig. 11-1 represents

increases the energy by a factor of two

Doubling only the spring constant of a vibrating mass-and-spring system produces what effect on the system’s mechanical energy?

38

Consider a 20.0-kg pendulum clock that keeps good time. If the clock is moved to a location where it weighs 74 N, how many minutes will the minute hand move in 1 h?

frequency

For a system in simple harmonic motion, which of the following is the number of cycles or vibrations per unit of time?

is maximum

A mass on a spring undergoes SHM. When the mass passes through the equilibrium position, its instantaneous velocity

midway between A and B

A mass is attached to a vertical spring and bobs up and down between points A and B. Where is the mass located when its potential energy is a minimum?