# Simple harmonic motion

## Definition

### In terms of the equation for position

**Simple harmonic motion** is defined as a form of periodic/oscillatory motion along a straight line, with the following form of equation describing the position coordinate as a function of time:

Here, is the resting position or mean position, is the *amplitude* of oscillation (in that it describes the maximum possible magnitude of displacement from the mean position), is a parameter controlling the frequency (in fact, is times the frequency of completing one full oscillation), is the time parameter, and is a phase angle.

As a consequence, we have the following descriptions of the velocity and acceleration functions:

and

### In terms of the differential equation it solves

Simple harmonic motion is a form of motion of an object/particle along a line subject to the constraint:

where is the position coordinate of the particle at time and is the acceleration (signed) of the particle at time .