Damped simple harmonic motion

A physical system in which some value oscillates above and below a mean value at one or more characteristicfrequencies. Such systems often arise when a contrary force results from displacement from a force-neutral positionand gets stronger in proportion to the amount of displacement, as in the force exerted by a spring that is stretched orcompressed or by a vibrating string on a musical instrument .

Observing the nature, we realize that many physical processes (for example, the Earth rotation around its polar axis) are repetitive, happening the facts cyclically. In these cases we speak about periodic motion and we characterize it by means of its period, which is the necessary time to complete a cycle, or by its frequency, which represents the number of complete cycles in the unit of time.


The system returns to equilibrium without oscillating.

Critically damped

The system returns to equilibrium as quickly as possible without oscillating.


The system oscillates (at reduced frequency compared to the undamped case) with the amplitude gradually decreasing to zero.


The system oscillates at its natural resonant frequency (ωo) without experiencing decay of its amplitude.