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Very roughly, when a system is under damped, it means that if it is disturbed from rest, it will oscillate back and forth. A good example of this is if you drop a heavy bag of cement into the bed of a pickup truck. Of course, the cement bag will make the truck bed go down, but it's the bounce back up that counts. If upon bouncing back in the up direction, the truck bed returns PAST it's original point of rest, it can be said to be underdamped, since it will bounce up past it's original point of rest, then start to go back down, and be effectively oscillating back and forth. If, on the other hand, the bed of the truck never bounces back past it's point of rest, and just gradually settles, it is over damped, and will not oscillate.

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