at the beginning, till some time a,
h(t) = 200 - 16t^2
due to free-fall. When h(t) reaches 200 - max cord extension, the springy characteristics of the cord enter in. If the cord could rebound 100%, the wave would have a constant amplitude.
h(t) = b - c*cos(k(t-a))
which allows for an offset cosine wave, starting at its minimum.
However, the amplitude dampens exponentially, so the curve for t>a would more likely be something like
h(t) = b - c*cos(k1(t-a))*e^(-k2*(t-a))
So, a parabola to start with, then a damped cosine wave.