Determine the equation of a sinusoidal function that would model this situation, assuming Owen reaches his first maximum at 6 seconds.

Question

Owen is jumping on a trampoline. When his feet hit the deck of the trampoline, the material depresses to a minimum 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

The Amplitude is 200 cm, since it reaches min. assuming it is zero at the middle. The Period is 10 seconds. at 6 seconds he reaches the first maximum. I would use a cosine function since the maximum is at zero seconds, so the there is a phase shift of 6 seconds we have. We have to reach max when t=6 sec or cos(t-6)

Since we have an amplitude of 200 cm we have 200cos(t-6). We now have to fix the period! Normally, the period of a cosine function is P=2*pi/b, where b is the coefficient of t. We want the period to be 10, so 10=2pi/b, solve for b we b=pi/5 so putting it together y=200cos((pi/5)(t-6)) When t=6, the inner () is zero, times pi/5 is zero and the cos(0) is 1 so we get y=200cm. When t=16(one-period later) we get 10 from the inner () 10(pi/5)= 2pi which give you maximum again! QED