Exam 13: Oscillations About Equilibrium

An oscillating system has a small amount of damping. It is observed that in the course of 20.0 s the amplitude has decreased from A to A/2. What additional time is required for the amplitude to decrease to A/10?

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?

Should the tuner on a radio have small or large damping?

A mass of 500 g is resting on a vertical spring with a force constant of 55.0 N/m. A mass of 250 g is dropped from a height of 12.0 cm onto the larger mass and sticks to it. What is the amplitude of the resulting oscillations?

A spring with a force constant of 2.00 N/m is attached to a mass of 75.0 g. The system has a small amount of damping. If the amplitude of the oscillations decreases from 10.0 mm to 5.00 mm in 15.0 s, what is the magnitude of the damping constant?

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?

The position of a mass that is oscillating on a spring is given by x = (12.3 cm) cos[(1.26 s^-1)t]. What is the speed of the mass when t = 0.805 s?

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

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?

Two players are enjoying a steady volley in a game of ping-pong, in which the motion of the ball is repeated regularly. Is the motion of the ball simple harmonic motion?

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

In designing buildings to be erected in an area prone to earthquakes, should you try to have a small or a large amount of damping?

FIGURE 13-1 -Curve C in Figure 13-1 represents

Increasing the damping constant beyond that required for critical damping makes the system approach equilibrium more quickly.

A thin hoop is supported in a vertical plane by a nail. What should the radius of the hoop be in order for it to have a period of oscillation of 1.00 s? The moment of inertia of a hoop of mass M and radius R about a point on its rim is 2MR².

The position of a mass that is oscillating on a spring is given by x = (17.4 cm) cos[(5.46 s^-1)t]. What is the period of this motion?

A mass is oscillating on a spring with an amplitude of 8.3 cm and a period of 4.6 s. Write an expression for its position, x, as a function of time, if x is equal to 8.3 cm at t = 0 s.

A mass of 0.150 kg is attached to a spring with a force constant of 3.58 N/m and undergoes simple harmonic oscillations with an amplitude of 7.50 cm. What is the total mechanical energy of the system?

In simple harmonic motion, the acceleration is proportional to

What is the length of a simple pendulum with a period of 2.00 s?