Damping is an influence within or upon an oscillatory system that has the effect of reducing or preventing its oscillation.
In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. Examples include viscous drag in mechanical systems, resistance in electronic oscillators, and absorption and scattering of light in optical oscillators.
The damping ratio \(\zeta\) is a dimensionless measure describing how oscillations in a system decay after disturbance.
\(\boxed{\zeta = \frac{\alpha}{\omega_0}}\)
where \(\omega_0\) is known as the resonant frequency or strictly as the undamped natural frequency, expressed in radians per second \((\textrm{rad}/\textrm{s})\); and \(\alpha\) is the neper frequency or the damping factor or the damping attenuation, expressed in nepers per second \((\textrm{Np}/\textrm{s})\).
The damping ratio \(\zeta\) is a system parameter that can vary from undamped \((\zeta = 0)\), underdamped \((0 < \zeta < 1)\) through critically damped \((\zeta = 1)\) to overdamped \((\zeta > 1)\). Systems that will oscillate are described as underdamped and those that will not are overdamped.
The special case of \(\zeta = 1\) is called critical damping and represents the case of the system that is just on the border of oscillation. It is the minimum damping that can be applied without causing oscillation.