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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.

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closed as off-topic by JMac, Ruslan, ZeroTheHero, John Rennie, Jon Custer Aug 22 '17 at 12:34

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  • $\begingroup$ Applications of overdamping?. $\endgroup$ – Ruslan Aug 21 '17 at 17:31
  • $\begingroup$ Hello, I have been through this page but I kind of found it to be vague and more of a convo between two people rather than something that I can understand as a newbie. $\endgroup$ – DmRo912 Aug 21 '17 at 17:35
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    $\begingroup$ This question seems to be more of an engineering question, and potentially doing homework for you. My only hint: What happens in objects where you don't know it's exact characteristics (like mass/stiffness may vary to an extent, such as in a car) and overshoot must be avoided? $\endgroup$ – JMac Aug 21 '17 at 17:36
  • $\begingroup$ The practical uses are situations where "overshooting" would be a disaster. To repeat the examples in the link, if a plane is landing and controlled by an autopilot, an overshoot which causes the plane to attempt to fly below the level of the runway probably won't end well! The same is true for controlling a machine tool (which is subject to random vibration caused by cutting the material) - if you cut too deep, you end up with scrap metal. Controlling an autonomous vehicle would be another example - you don't want to overshoot when stopping in a confined space for example. $\endgroup$ – alephzero Aug 22 '17 at 5:10
  • $\begingroup$ @alephzero how about the automatic control of a foundry crucible pouring molten iron! Imagine what overshoot might lead to. $\endgroup$ – docscience Aug 22 '17 at 22:00
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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.

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  • $\begingroup$ Every textbook I've seen defines the critical damping factor as $1.0$ (exactly), not $\sim 0.7$. Is $0.7$ an approximation to $1/\sqrt{2}$, in some alternative formulation of the math? Or is it just an empirical number used in some application area (control engineering or whatever)? $\endgroup$ – alephzero Aug 22 '17 at 5:12
  • $\begingroup$ @alephzero thanks. Not the first time I've forgotten that. Corrections made! $\endgroup$ – docscience Aug 22 '17 at 21:57

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