Question

At a certain harbour, the tides cause the ocean surface to rise and fall a distance d(from highest level to lowest level) in simple harmonic motion, with a period of 12.5h. How long does it take for the water to fall a distance 0.250d from its highest level?

Answer 1

h = (d/2) cos (2 pi t/ 12.5)

h = .25 d
so
.5 = cos theta
theta = 60 degrees = pi/3
so
2 pi t/12.5 = pi/3
t = 12.5/6
= 2.08 hours