Finding sinusoidal function

Question

Owen is jumping on a trampoline. When his feet hit the deck of the trampoline, the material depresses to a minimum height of 2cm. On average, Owen is reaching a maximum height of 200cm every 10 seconds. Determine the equation of a sinusoidal function that would model this situation, assuming Owen reaches his first maximum at 6 seconds.

Answer 1

This seems to be a little ambiguous but I'm guessing it's like this:

where we are measuring off the trampoline's relaxed surface position. We can use the equation:

h(t) = Acos(B(t - C)) + D

where:

A is the Amplitude, in this case that would be 200 cm from the relaxed position plus the 2 cm initial deflection or 202.

B is derived from the period and is in fact (2π)/period = (2π)/10 = π/5

C is the time shift and is 6

and D is the vertical shift which in this case is -2

So: h(t) = 202cos(π/5(t - 6)) - 2