Oscillation

x = A cos(ω t)
v = -A ω sin(ω t)
a = -A ω² cos(ω t)
a = -ω²x
Equilibrium: mg = k Δx

BOING, BOING!

This simulator can model Simple Harmonic Motion, or an oscillator with damping.

You can drag the ball on the end of the string to start the oscillation again. Damping is fraction of velocity lost per second, so 0.5 is 50% of the velocity lost per second. Also try varying the string constant and the mass. (Warning: the view changes scale so that the equilibrium is aways in the centre of the screen vertically).