AP calculus word problem?

Question

A buoy oscillates in simple harmonic motion y=A cos wt
aswaves move past it. The buoy moves a total of 3.5 feet (vertically) from its low point to its high point. It returns to its high point every 10 seconds.

a.) write an equation describing the motion of the bouyif its is at its high point at t=0

b) determine the velocity of the buoy as a function of t


Any help would be greatly apreciated or a formular. Thanks

Answer 1

The cosine function ranges from a minimum of -1 to a maximum of 1. So if
y = A cos(wt), y ranges from -A to A, that is, a distance of 2A. Your problem gives this distance as 3.5 feet. Solve for A.

If the buoy returns to its high point every 10 seconds, its motion has a period of 10 seconds. There is a relationship between period T and frequency w:

w = 2π/T

For part b, the velocity is given by dy/dt.

Answer 2

♦ thus A=3.5/2 = 1.75 ft is mentioned as amplitude, boy’s period being T=10 s,
cyclic frequency is w=2pi/T and y=1.75 cos(pi*t/5);
♥ and velocity y’=-(1.75*pi/5) sin(pi*t/5);