Simple Harmonic Motion


In each of the cases below there is something that is oscillating, it vibrates back and forth or up and down.

Each of these systems is demonstrating Simple Harmonic Motion (SHM).

SHM Characteristics

The equilibrium point is where the object comes to rest, in the simple pendulum it at its lowest point.

If we displace the object by a displacement of x there will be a force that brings the object back to the equilibrium point. We call this the restoring force and it always acts in the opposite direction to the displacement.

We can represent this as:


Since  F=ma we can also write:


For an object to be moving with simple harmonic motion, its acceleration must satisfy two conditions:

*The acceleration is proportional to the displacement

*The acceleration is in the opposite direction to the displacement (towards the equilibrium point)


The following equations are true for all SHM systems but let us use the simple pendulum when thinking about them.

The pendulum bob is displaced in the negative direction when at point 1, it is released and swings through point 2 at its maximum speed until it reaches point 3 where it comes to a complete stop. It then swings to the negative direction, reaches a maximum speed at 4 and completes a full cycle when it stops at 5.