Question

At a certain harbor, 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 12.5 h. How long does it take for the water to fall a distance 0.250d from its highest level?

Answer 1

The motion is simple harmonic motion and if you model this as a sin wave of period 12.5 and amplitude d/2
the height of the water from its mean position is d/2 cos(theta) ( maximum at t= 0).

Therefore, when it is 0.250d from maximum this is d/4 ABOVE the minimum.

This means -  
d/2 cos(theta) = d/4

=> cos(theta) = 1 / 2

=> theta = 60 degrees

and it represents a fraction 60/360 of the whole period ( 1/6)

So, the time taken to fall a distance 0.250d from its highest level = (60/360) * 12.5 h = 2.08 hours.