Math:Trig.!!!!
posted by Claries on .
You (safely) bungee jump from a 200feet tall bridge in your town. Your distance above the water's surface depends on the time since you jumped. Sketch a reasonable graph.

at the beginning, till some time a,
h(t) = 200  16t^2
due to freefall. 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.
for t>a,
h(t) = b  c*cos(k(ta))
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(ta))*e^(k2*(ta))
So, a parabola to start with, then a damped cosine wave.