In physics, **damping** is an effect that reduces the amplitude of oscillations in an oscillatory system (except for mass-dominated systems where √2), particularly the harmonic oscillator. This effect is linearly related to the velocity of the oscillations. This restriction leads to a linear differential equation of motion, and a simple analytic solution.

In mechanics, damping may be realized using a dashpot. This device uses the viscous drag of a fluid, such as oil, to provide a resistance that is related linearly to velocity. The damping force *F*_{c} is expressed as follows:

where *c* is the *viscous damping coefficient*, given in units of newton seconds per meter (N s/m) or simply kilograms per second. In engineering applications it is often desirable to linearize non-linear drag forces. This may by finding an equivalent work coefficient in the case of harmonic forcing. In non-harmonic cases, restrictions on the speed may lead to accurate linearization.

Generally, damped harmonic oscillators satisfy the second-order differential equation:

where *ω*_{0} is the undamped angular frequency of the oscillator and *ζ* is a constant called the damping ratio.

The value of the damping ratio *ζ* determines the behavior of the system. A damped harmonic oscillator can be:

*Overdamped*(*ζ*> 1): The system returns (exponentially decays) to equilibrium without oscillating. Larger values of the damping ratio*ζ*return to equilibrium more slowly.*Critically damped*(*ζ*= 1): The system returns to equilibrium as quickly as possible without oscillating. This is often desired for the damping of systems such as doors.*Underdamped*(0 <*ζ*< 1): The system oscillates (at reduced frequency compared to the*undamped*case) with the amplitude gradually decreasing to zero.*Undamped*(*ζ*= 0): The system oscillates at its natural resonant frequency (*ω*_{o}).

Read more about Damping: Definition, Example: Mass–spring–damper, Alternative Models

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