Question

The propeller of a boat at dock in the ocean will rise and fall with the waves. On a particularly wavy night, the propeller leaves its resting position and reaches a height of 2m on the peaks of the waves and -2m in the troughs. The time between the peak and the trough is approximately 3 seconds. Determine the equation of a sinusoidal function that would model this situation assuming that at equation , the propeller is at its resting position and headed towards the peak of the next wave.

Answer 1

h=2 m. = Ht. or amplitude of the wave.

P = 2 * 3s = 6 s. = The period or time
for i cycle.

F = 1/P = 1/6 c/s = 1/6 Hz = Frequency of the wave.

h = hmax*sinWt.
h = 2*sinWt.
W = 2pi*F = 2piRad/c * (1/6)c/s = 2pi/6 = pi/3 Rad/s.

Eq: h = 2*sin((pi/3)t)