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It starts at undamped, proceeds to underdamped, then critically damped, then overdamped. Undamped Is the case where = corresponds to the undamped simple harmonic oscillator, and in that case the solution looks like (), as expected. This case is extremely rare in the natural world with the closest examples being cases where friction was ...
If a frictional force proportional to the velocity is also present, the harmonic oscillator is described as a damped oscillator. Depending on the friction coefficient, the system can: Oscillate with a frequency lower than in the undamped case, and an amplitude decreasing with time (underdamped oscillator).
The damped natural frequency is less than the undamped natural frequency, but for many practical cases the damping ratio is relatively small and hence the difference is negligible. Therefore, the damped and undamped description are often dropped when stating the natural frequency (e.g. with 0.1 damping ratio, the damped natural frequency is ...
Damped oscillation is a typical transient response, where the output value oscillates until finally reaching a steady-state value. In electrical engineering and mechanical engineering, a transient response is the response of a system to a change from an equilibrium or a steady state. The transient response is not necessarily tied to abrupt ...
An undamped spring–mass system is an oscillatory system. Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum and alternating current. Oscillations can be ...
where = is called the damping ratio of the system, = is the natural angular frequency of the undamped system (when c=0) and = is the angular frequency when damping effect is taken into account (when ).