Damped Harmonic Oscillator

Driven oscillator

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Damping Coefficient

When a damped oscillator is subject to a damping force which is linearly dependent upon the velocity, such as viscous damping, the oscillation will have exponential decay terms which depend upon a damping coefficient. If the damping force is of the form

then the damping coefficient is given by

This will seem logical when you note that the damping force is proportional to c, but its influence inversely proportional to the mass of the oscillator.

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Underdamped Oscillator

 Damped Oscillator Further details for underdamped case
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Underdamped Oscillator

When a damped oscillator is underdamped, it approaches zero faster than in the case of critical damping, but oscillates about that zero.
 The equation is that of an exponentially decaying sinusoid. The damping coefficient is less than the undamped resonant frequency . The sinusoid frequency is given by but the motion is not strictly periodic.
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