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 12.4 h. how long does it take for the water to fall a distance 0.250d from its highest level?

T = 12.4 h, x (t) =.250 d (displacement)

The total amplitude is half of the distance d from the highest to lowest level.

Using the equation x (t) = x (m) cos (wt + φ), we get:

.250d =.5d cos (wt + φ)

To find w, use the equation w = 2π / T

.250d =.5d cos ((2π / 12.4) t + φ)

.250d =.5d cos ((2π / 12.4) t + 0)

Solve the equation for t.

.250d /.5d = cos ((2π / 12.4) t)

arccos (.5) = 2π / 12.4 * t

arccos (.5) * 12.4 / 2 / π = t

t = 2.066666 hours