= Oscillator
An <oscillator> is a system capable of repeated motion or variation about a central state. A mass $m$ on an ideal <spring> with <spring constant> $k$ satisfies
$$
m\ddot x+kx=0,\qquad \omega_0=\sqrt{k/m}.
$$
The restoring <force> accelerates the mass toward zero <displacement>; <inertia> carries it through that point, producing <simple harmonic motion>. The <kinetic energy> is largest at zero <displacement>, and the elastic <potential energy> is largest at the turning points.
Real <oscillators> can include <damping>, external driving and <anharmonicity>. A <damped harmonic oscillator> distinguishes the free transient from the forced periodic response, and a <coupled oscillator> adds exchange of <energy> with another dynamical coordinate. This makes an <oscillator> useful both as a physical device and as an approximation to small disturbances of much more complicated systems.
Back to article page
