The buoy oscillates in simple harmonic motion .

Where  is amplitude,  is angular velocity, and  is time.

The buoy moves total distance is  feet.

The buoy returns its high point for every  seconds.

(a)

Write an equation describing the motion of the buoy if it is at its high point at .

The amplitude at high point is .

The angular velocity is .

.

Substitute  and  in .

The equation is .

(b)

Determin the velocity of the buoy as a function of .

Velocity of an object is rate of change of the displacement.

Apply derivative on each side with respect to .

.

(a) The equation is .

(b) The velocity of buoy is .