Exam 15: Oscillations

A simple harmonic oscillator consists of a mass m and an ideal spring with spring constant k. The particle oscillates as shown in (i) with period T. If the spring is cut in half and used with the same particle, as shown in (ii), the period will be:

A particle is in simple harmonic motion along the x axis. The amplitude of the motion is x_m. At one point in its motion its kinetic energy is K = 5J and its potential energy (measured with U = 0 at x = 0) is U = 3J. When it is at x = x_m, the kinetic and potential energies are:

The acceleration of a body executing simple harmonic motion leads the velocity by what phase?

A weight suspended from an ideal spring oscillates up and down with a period T. If the amplitude of the oscillation is doubled, the period will be:

A simple pendulum consists of a small ball tied to a string and set in oscillation. As the pendulum swings the tension in the string is:

A simple pendulum has length L and period T. As it passes through its equilibrium position, the string is suddenly clamped at its mid-point. The period then becomes:

Two identical undamped oscillators have the same amplitude of oscillation only if:

The displacement of an object oscillating on a spring is given by x(t) = x_mcos( $\omega$ t + $\phi$ ). If the initial displacement is zero and the initial velocity is in the negative x direction, then the phase constant $\phi$ is:

It is impossible for two particles, each executing simple harmonic motion, to remain in phase with each other if they have different:

The amplitude of oscillation of a simple pendulum is increased from 1 $\degree$ to 4 $\degree$ . Its maximum acceleration changes by a factor of:

Below are sets of values for the spring constant k, damping constant b, and mass m for a particle in damped harmonic motion. Which of the sets takes the longest time for its mechanical energy to decrease to one-fourth of its initial value?

Two uniform spheres are pivoted on horizontal axes that are tangent to their surfaces. The one with the longer period of oscillation is the one with:

The rotational inertia of a uniform thin rod about its end is ML²/3, where M is the mass and L is the length. Such a rod is hung vertically from one end and set into small amplitude oscillation. If L = 1.0 m this rod will have the same period as a simple pendulum of length:

A mass-spring system is oscillating with amplitude A. The kinetic energy will equal the potential energy only when the displacement is

A sinusoidal force with a given amplitude is applied to an oscillator. To maintain the largest amplitude oscillation the frequency of the applied force should be:

In simple harmonic motion, the displacement is maximum when the:

An object is undergoing simple harmonic motion. Throughout a complete cycle it:

A simple pendulum of length L and mass M has frequency f. To increase its frequency to 2f:

A sinusoidal force with a given amplitude is applied to an oscillator. At resonance the amplitude of the oscillation is limited by:

Both the x and y coordinates of a point execute simple harmonic motion. The frequencies are the same but the amplitudes are different. The resulting orbit might be: