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ok, so now we have a velocity plot. let's examine what it tells us.
the job of a damper is to control the motion of the car. without a damper, a sprung mass will continue to oscillate (bounce up and down). the damper's job is to damp that motion, to gradually slow the controlled mass.
when something is critically damped, it will return to equilibrium without going past it. when something is underdamped, the mass will go past equilibrium at least once before returning. when something us underdamped, it will take too long to return to equilibrium.
in carspek, underdamped means more bounces when you hit a bump. overdamped means the car won't recover fast enough after a bump; this can cause a 'jacking' effect where multiple bumps in a row will cause the suspension to bottom out. critical damping means the car will hit the bump and immediately return to its proper ride height.
we want something that is slightly underdamped. the a damping ratio of 1 is critical; less than 1 is underdamped, greater than 1 is overdamped.
for road cars, the damping ratio is generally around .3 - .5. for sports / track cars, it's around .7. look at the graph below to see what these different damping ratios look like.
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