Damping Coefficient

Damping is experienced by most oscillatory systems such as harmonic oscillators. These systems, when displaced from their equilibrium position, experience a restoring force proportional to their displacement. If a frictional force proportional to the velocity is also applied, the system exhibits damped harmonic oscillation. The system’s damping coefficient is a measure of how quickly it returns to rest as the frictional force dissipates its oscillation energy.

Four damping scenarios exist. The first is the hypothetical case of an undamped system, where no frictional force exists, and oscillations continue indefinitely. Next is the realistic and common case of underdamping that could be observed, for example, in a playground swing. If lifted and released, it will swing and overshoot its rest position with arcs of diminishing amplitude as air and bearing resistances reduce its speed.

Other systems, such as door closers or railway buffers, are overdamped, typically using a viscous fluid; the displaced mass returns slowly to its rest position with no overshoots.

Systems can also be critically damped, which is a desirable state for many applications such as car suspension assemblies. Here, the displaced mass does not oscillate, and just fails to overshoot. Critically damped systems return to equilibrium in the shortest possible time.

Damping is also applied to electronic systems. For example, a resonant tuned circuit can be damped with an impedance.