Wave Motion

Question

A buoy oscillates in simple harmonic motion as waves go past. At a given time it is noted that the buoy moves a total of 3.5 feet from its low point to its high point, and that it returns to its high point every 10 seconds. Write an equation that describes the motion of the buoy if it is at its high point at t=0.

(Note: Rationalize and think thoroughly throughout this solving process, don't stress your mind in a negative way. Just relax and look over the information carefully.)

Answer 1

since the amplitude is half the (max-min), and it oscillates about the middle, we can get that by using

y=7/4 cos(t) + 7/4

since cos(t) starts out at its max at t=0. But, that has period 2π. We're almost there. We want a period of 10, so since cos(kt) has period 2π/k,

y = 7/4 cos(2π/10 t) + 7/4

is our function.