If an oscillation is completely undamped, the oscillation will go on forever. In practice however, all oscillations must encounter some damping forces (e.g. air resistance, friction). Damping saps the oscillation’s energy continuously, causing its amplitude to decrease continuously over time.
The behavior of damped oscillations has been studied extensively, in particular for the case of the damping force being proportional to the velocity. It turns out that there are three distinct outcomes depending on the degree of damping.
If the oscillation is subjected to light damping (a.k.a. underdamping), the amplitude of the oscillation decreases gradually over time. The displacement-time graph is roughly enveloped by an exponential decay function. The higher the amount of damping, the faster the rate of decay and the steeper the slope of the exponential decay function.
Lengthening of the Period
Damping causes an oscillation to have a longer period than if it were undamped. However, the lengthening of the period under very light damping is very small. In fact, the lengthening of period is more often than not neglected in the H2 syllabus.
If the oscillation is subjected to heavy damping (a.k.a. overdamping), the oscillator returns slowly to the equilibrium position without ever going past the equilibrium position. In that sense, heavy damping totally completely prevented any oscillation.
Critical damping is the transition point between light and heavy damping. Critical damping causes a displaced oscillator to return to the equilibrium position in the shortest amount of time and without crossing the equilibrium position. Because of this, critical damping is the design objective in many engineering applications (e.g. shock absorbers, car suspension systems etc.).