Damped Oscillation

Oscillations occur in all types of system; mechanical, electrical and thermal. The behaviour of oscillating systems is often of interest in a diverse range of disciplines that include control engineering, mechanical engineering, structural engineering, and electrical engineering.

Mechanical systems make a good starting point for understanding oscillation, as mechanical oscillation is plainly visible. Imagine, for example, a mass suspended from a spring. If the mass is pulled down and then released, the spring will attempt to return to its equilibrium position, but the speed of the travelling mass will cause it to overshoot until gravity pulls it downwards again. The spring-mass system will be oscillating as these bounces continue.

In an ideal, lossless system, this would continue indefinitely without reduction of bounce amplitude; a condition of undamped oscillation. In reality, however, air resistance would gradually reduce the bounce amplitude, which would decay until the mass comes to rest – under-damped oscillation. Conversely, if the experiment were conducted within a tank of viscous fluid, the weight would slowly return to the equilibrium position and never overshoot – an overdamped condition.

If the mass just returns to equilibrium with no overshoot, the system is critically damped. Critically damped systems, unlike overdamped ones, return to equilibrium in the shortest possible time.

Electronic circuits that include both inductive and capacitive elements can be made to oscillate; this oscillation will be damped by resistance that will also inevitably be present in the circuit.