Damped Harmonic Oscillator
Explanation of motion equation notationDriven 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 
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Underdamped Oscillator

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Underdamped OscillatorWhen a damped oscillator is underdamped, it approaches zero faster than in the case of critical damping, but oscillates about that zero.

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