In driven (or forced) harmonic motion, the system experiences a sinusoidally oscillating force. The response of the system depends on how the frequency of the force compares to the natural oscillation frequency of the system.

A good example of such a system is a playground swing. When you push a kid on a swing, you match the frequency of your pushes to the frequency of the swinging kid - this is the most effective way to get (and keep) the kid going.

That is known as resonance - when the driving frequency matches the natural frequency of the system (the resonance frequency) then the oscillation amplitude can grow to be quite impressive, even when the driver has a relatively small amplitude.

The phase relationship between the driving force and the oscillating mass is interesting to observe:

• Below resonance they're in phase
• At resonance they're 90 degrees out of phase
• Above resonance they're 180 degrees out of phase