Exam 14: Oscillations

A mass of 0.50 kg is attached to a massless spring with a spring constant k = 600 N/m (see figure above). The system rests on a level, friction-free surface and is initially at rest. A second mass of 0.20 kg makes an elastic head-on collision with the mass attached to the spring; thereafter, the oscillating system vibrates with an amplitude of 0.25 m. What was the incident speed of the second mass?

An object is moving with simple harmonic motion. When the object is displaced 5 cm from its equilibrium point, its velocity is 15.0 cm/s. Calculate the amplitude of motion if its period of motion is 3.0 s.

An oscillator has a quality factor of 100. By what percentage does its energy decrease in each cycle?

A particle moving with simple harmonic motion has a maximum displacement of +12)0 cm. The particle moves from its maximum positive to its maximum negative displacement in 2.25 s. The motion starts when the displacement is x = +12.0 cm. The time for the particle to move to x = -6.00 cm is

A giant simple pendulum has a time period of 5.00 s at a particular place. If the time period is changed to 4.65 s by shortening the string by 1.0 m, calculate the acceleration due to gravity at this place.

For a simple pendulum to have a period of 1 s it must have a length of

Use the following to answer question : -The graph shows the displacement of an oscillator as a function of time. The oscillator that is undamped is

The acceleration of a particle moving with simple harmonic motion is given by A = -16.0x, Where x is in meters and a is in meters per second squared. The period of the motion is

The solution to the differential equation of a damped oscillator, for the case in which the damping is small, is X = A₀e^-(b/2m)t cos( $\omega$ 't + $\delta$ ) The phase constant $\delta$ is determined by the

Use the following to answer question : -The object in the diagram is in circular motion with frequency f. At t = 0 it was at (A, 0). The y component of its velocity is given by

A 2-kg mass oscillates in one dimension with simple harmonic motion on the end of a massless spring on a horizontal frictionless table according to X = (6/ $\pi$ ) cos( $\pi$ t + 3 $\pi$ ) Where the units are SI. The total mechanical energy of this system is

The force constant for a simple harmonic motion is k and the amplitude of the motion is A. The maximum value of the potential energy of a mass m oscillating with simple harmonic motion is

A spring vibrates in simple harmonic motion according to the equation X = 15 cos $\pi$ t. Where x is in centimeters and t is in seconds. The total number of vibrations this body makes in 10 s is

A body oscillates with simple harmonic motion according to the equation X = 6.0 cos(3t + $\pi$ /3) Where the units are SI. The speed of the body when it has a displacement of 3 m is

Use the figure to answer the problem. A spring of negligible mass and spring constant k is attached to the wall on one end, and the other end is attached to the center of mass axis of a solid sphere of mass m and radius r. The spring is stretched a distance A from equilibrium and let go. The sphere rolls freely on a smooth surface. -What is the rotational kinetic energy when the sphere is at the equilibrium position?

A pendulum has simple harmonic motion provided that

A 0.5-kg mass is suspended from a massless spring that has a force constant of 79 N/m. The mass is displaced 0.1m down from its equilibrium position and released. If the downward direction is negative, the displacement of the mass as a function of time is given by

In the laboratory, a stick 1 m long is pivoted at various points to illustrate the motion of a physical pendulum. A plot of the period versus the distance of the pivot point from the center of mass is shown. The data presented demonstrate which of the following?

Near resonance, if the damping is small (large Q), the oscillator

The instantaneous speed of a mass undergoing simple harmonic motion on the end of a spring depends on