We have been given this task of preparing some small research on critical damping and comparing its behaviour and uses with over-damping. I am done with everything else but have been unable to find practical uses of over damping. It'd be great if someone could explain where it's desired.
closed as off-topic by JMac, Ruslan, ZeroTheHero, John Rennie, Jon Custer Aug 22 '17 at 12:34
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'Critical Damping' is a descriptive term given to 2nd order linear dynamic systems where the damping factor is ~ 1.0. And for the 2nd order system critical damping provides a settling towards your equilibrium point as quickly as possible without overshoot or bouncing about the equilibrium state: a smooth however rapid transition. If you specify critical damping you might be trying to get your system to settle with an asymptotic trajectory as quickly as possible like targeting a data track on a disk drive for example.
But with overdamping you are further reducing speed for smoothness of settling to your equilibrium value. Any example of public transportation braking systems would be good examples where the desire is to provide the rider with comfort over the speed of coming to a stop. Like a train, elevator or automobile.