Physics Formulas

Simple Harmonic Motion

Definition of Simple Harmonic Motion

Simple Harmonic Motion in physics or SHM is defined as oscillating motion of an object about an fixed point such that the acceleration (a) of the object is:

  1. proportional to the displacement (x) from the fixed point,
  2. always directed towards the fixed point

The definition of Simple Harmonic Motion (SHM) can be summarized in the Simple Harmonic Motion equation below.

Formula for Simple Harmonic Motion

Simple Harmonic Motion equation



Simple Harmonic Motion - Acceleration = acceleration (unit is ms -2)
Simple Harmonic Motion - displacement = displacement (unit is m)
Angular frequency = angular frequency (unit = rad s -1)

In another word, Simple Harmonic Motion (SHM) is a form of periodic motion in which a point or body oscillates along a line about a central point in such as way that it ranges an equal distance on either side of the central point and that its acceleration towards the central point is always proportional to its distance from it.

Visualizing Simple Harmonic Motion in Physics

One way to visualize Simple Harmonic Motion is to imagine a point rotating around a circle of radius r at a constant angular velocity Angular frequency. If the distance from the center of the circle to the projection of this point on a vertical diameter is y at time t, this projection of he point will move about the center of the circle with simple harmonic motion. A graph of y against t will be a sine wave, whose equation is:

Simple Harmonic Motion equations