The gradual reduction or suppression of the oscillatory behaviour of a process variable such as temperature, pressure, and liquid level in a controlled system or process. Damped harmonic oscillators satisfy the second-order differential equation of the form:
where ωo is the undamped angular frequency and ς is the damping ratio. Critical damping (ς = 1) is where response to a change is abrupt, in which there is no overshoot of the set point. Under-damping (0 < ς <1) occurs when there is overshoot, while over-damping (ς > 1) occurs when the response is slower than critical damping. An undamped system (ς = 0) corresponds to its natural resonant frequency (ωo).