70. Parametric Oscillation

Parametric oscillation occurs when one of the parameters of the system is varied. A child can "pump" a swing by standing and raising and lowering her center of mass periodically, changing the length of the pendulum. The child pumps at twice the pendulum frequency, generating a sub harmonic.

A very simple demonstration of parametric oscillation is the coupling of the pendulum mode to a mass on a spring. When the spring frequency is approximately twice the swinging frequency (pendulum mode), the spring mode parametrically drives the pendulum mode, but the pendulum motion causes the tension in the spring to vary at twice the pendulum frequency, and therefore resonantly drives the spring mode. The transfer of energy between these two modes is impressive.