Dampa

Meet Dampa, a bouncing spring whose every swing is a little smaller than the last.

A real oscillator loses energy, to air drag, friction or internal heating. For light damping, where the drag is proportional to speed, the motion is still an oscillation at angular frequency ω, but its amplitude shrinks exponentially: x(t) = Ae^(−γt) cos(ωt). The peaks lie on a decaying envelope Ae^(−γt), and the damping rate γ sets how quickly it falls.

Each interval of 1/γ shrinks the amplitude by a factor of e, about 2.7. With γ = 0.5 per second, after 2 seconds the swings are about 37 percent of their starting size, and after 6 seconds about 5 percent.

Damping is often designed on purpose. Car shock absorbers damp the bounce of the springs so the ride settles quickly, and buildings in earthquake zones use dampers. Engineers often aim for critical damping, the fastest return without overshoot, as in many door closers.

With heavy damping the system does not oscillate at all. And the damping also slightly lowers the oscillation frequency compared with the undamped case.