Anyone who has watched a child swinging on a playground swing has witnessed a vibrating system in resonance. The phenomenon of resonance appears often in everyday life; another example is the vibration of the body panels of a car containing a loud car stereo system. In the case of the child on the swing as the "vibrating system," resonance allows for fun and excitement, while in the case of the car stereo the resonance of the body panels is a source of annoyance. Three main concepts underlie vibrating systems and resonance: restoring force, natural frequency, and frequency matching.

A vibrating system is any system that exhibits a "restoring force." In the case of the child on a swing, the restoring force is the force of gravity that constantly acts to restore the swing to its place at the bottom of its arc...