Exam 15: Oscillations

Five particles undergo damped harmonic motion. Values for the spring constant k, the damping constant b, and the mass m are given below. Which leads to the smallest rate of loss of mechanical energy?

An angular simple harmonic oscillator:

A particle moves in simple harmonic motion according to x = 2cos(50t), where x is in meters and t is in seconds. Its maximum velocity is:

A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m. If the system has an energy of 6.0 J, then the amplitude of the oscillation is:

The angular displacement of a simple pendulum is given by θ(t) = θ_m cos (ωt + φ). If the pendulum is 45 cm in length, and is given an angular speed dθ/dt = 3.4 rad/s at time t = 0, when it is hanging vertically, what is θ_m?

A 0.20-kg object mass attached to a spring whose spring constant is 500 N/m executes simple harmonic motion. If its maximum speed is 5.0 m/s, the amplitude of its oscillation is:

In simple harmonic motion:

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

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

A particle is in simple harmonic motion with period T. At time t=0 it is halfway between the equilibrium point and an end point of its motion, travelling toward the end point. The next time it is at the same place is:

The amplitude of any oscillator will be doubled by:

A block attached to a spring oscillates in simple harmonic motion along the x axis. The limits of its motion are x = 10 cm and x = 50 cm and it goes from one of these extremes to the other in 0.25 s. Its amplitude and frequency are:

For an oscillator subjected to a damping force proportional to its velocity:

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:

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:

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

In simple harmonic motion, the restoring force must be proportional to the:

A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m. If the oscillation is started by elongating the spring 0.15 m and giving the block a speed of 3.0 m/s, then the amplitude of the oscillation is:

Frequency f and angular frequency $\omega$ are related by

An angular simple harmonic oscillator is displaced 5.2 x 10^-2 rad from its equilibrium position. If the torsion constant is 1200 N∙m/rad, what is the torque?