Oscillations damps according to a characteristic time. This demonstration is geared to demonstrating that damping using lasers (which tend to make demos more exciting at their mere inclusion). The system at rest looks like:
The equilibrium point, full-amplitude, and half-amplitude points are marked (lasers fixed on the full- and half-amplitude markings). Pull the mass down to the full-amplitude marking so that the laser is barely eclipsed, as shown:
Release and let it go! The lasers make it very clear when the oscillations have decayed to half their original amplitude.
When it goes past, the mass ceases to eclipse the top laser.
For reference, this is the full set up: