Damped Harmonic Oscillator

Explanation of motion equation notation

Driven oscillator

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.

Underdamped Oscillator

Underdamped Oscillator

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.