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Heavy Damping

Vibrations & Waves

Damped Harmonic
Motion

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Heavy Damping

Heavy Damping occurs when Q < 1/2. The motion is described by:


(see the maths of heavy damping)

Physically, as might be expected, the system slowly moves to equilibrium. For example, if a door closing mechanism is heavily damped, when released from the open position the door slowly closes, moving to the equilibrium position without oscillating.

The graph of position against time would look like this:

Example

An undamped saloon door swings backwards and forwards with a frequency of 0.5 Hz. If a damping mechanism is added with Q = 0.2 what fraction of the way has the door closed after 3.5 seconds?

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