Unit 6: Oscillations

For a mass-spring system, the period of oscillation is:

The position of a 0.5 kg mass on a spring is x(t) = 0.1cos(4πt). What is the maximum kinetic energy?

The differential equation for a simple harmonic oscillator is [math]. The general solution is

A physical pendulum consists of a uniform rod of mass M and length L pivoted at one end. Its period of small oscillations is

A spring-mass system oscillates as [math] meters. The maximum acceleration is

In a damped oscillator governed by [math], critical damping occurs when

The energy of a simple harmonic oscillator with amplitude A, mass m, and angular frequency ω is

Two identical springs each with constant k connected in series have effective spring constant

A torsional pendulum has angular displacement [math]. The amplitude decreases by a factor of [math] in time

The position of a simple harmonic oscillator is [math]. The angular frequency is

A pendulum of length L on a planet with gravitational acceleration g has period T. If taken to a planet with 4g, the length must be changed to what value to keep the same period?

An underdamped oscillator has solution [math] where [math]. The damped frequency is

For a mass on a spring, the phase relationship between displacement and velocity is

The period of a mass on a spring is given by T = 2π√(m/k). If the mass is quadrupled, the period:

In simple harmonic motion, where is the kinetic energy maximum?

A mass on a spring has amplitude A and angular frequency ω. The maximum speed of the mass is:

In SHM, the acceleration of the object is:

The period of a physical pendulum is T = 2π√(I/mgh), where h is the distance from the pivot to the center of mass. Compared to a simple pendulum of length h, the physical pendulum has:

In a damped oscillation, the amplitude:

If the spring constant is doubled and the mass is halved, the frequency of oscillation: