What is "damping ratio"

n. (context physics mathematics English) A dimensionless measure of the damping in second-order linear dynamic system, appearing as the term $zeta$ in the generalised equation of motion for such a system, $ddot\{q\}\; +\; 2zetaomega\_ndot\{q\}\; +\; omega\_n^2\; q\; =\; F.$

In engineering, the damping ratio is a dimensionless measure describing how oscillations in a system decay after a disturbance. Many systems exhibit oscillatory behavior when they are disturbed from their position of static equilibrium. A mass suspended from a spring, for example, might, if pulled and released, bounce up and down. On each bounce, the system is "trying" to return to its equilibrium position, but overshoots it. Sometimes losses (e.g. frictional) damp the system and can cause the oscillations to gradually decay in amplitude towards zero or attenuate. The damping ratio is a measure of describing how rapidly the oscillations decay from one bounce to the next.

The behaviour of oscillating systems is often of interest in a diverse range of disciplines that include control engineering, mechanical engineering, structural engineering, and electrical engineering. The physical quantity that is oscillating varies greatly, and could be the swaying of a tall building in the wind, or the speed of an electric motor, but a normalised, or non-dimensionalised approach can be convenient in describing common aspects of behavior.