Free oscillations

When an oscillator is simply displaced from its equilibrium position and let go, with nothing further acting on it besides its own restoring force, it oscillates at a frequency equal to its own natural frequency -- the frequency fixed purely by its own inertia and restoring-force properties (e.g. $\sqrt{k/m}$ for a spring-mass system or $\sqrt{g/l}$ for a pendulum). This is called free oscillation or free vibration. In the ideal (no energy loss) case, the amplitude, frequency, and total energy of the vibrating object all remain constant indefinitely. Examples include a struck tuning fork ringing on its own, a plucked stretched string, a simple pendulum swinging (ignoring air resistance), and a displaced spring-mass system oscill …