Oscillations

Defines linear simple harmonic motion with angular frequency omega.

Gives position at time t for an oscillator with amplitude A and initial phase phi.

Gives velocity as a function of displacement x from the mean position.

Gives acceleration directed towards the mean position at displacement x.

Gives maximum speed at the mean position and maximum magnitude of acceleration at extreme positions.

Gives the kinetic energy of an oscillator at displacement x from the mean position.

Gives the potential energy of an oscillator at displacement x from the mean position.

Gives the constant total mechanical energy of an undamped simple harmonic oscillator.

Gives the oscillation period and angular frequency of an inertia mass m loaded on a spring of stiffness k.

Gives the time period of a simple pendulum of length L undergoing small angular oscillations.

Gives the resultant amplitude of two parallel SHMs of identical frequency differing in phase by phi.

Gives the exponential decay of amplitude over time under damping constant b.

Gives the time period of vertical oscillations of a liquid column of total length L in a uniform U-tube.

Gives the time period of vertical oscillations for a body of mass m and cross-section A floating in liquid of density rho.