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
.