Viscous damping force is directly proportional to relative velocity
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Critical damping just prevents vibration or is just sufficient to allow the object to return to its rest position in the shortest period of time.
The automobile shock absorber is an example of a critically damped device. Additional damping causes the system to be overdamped, which may be desirable, as in some door closers.
The vibrations of an underdamped system gradually taper off to zero.
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The viscous damping force is proportional to the first power of the velocity across the damper, and it always opposes the motion, so that the damping force is a linear continuous function of the velocity
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