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11 December, 10:06

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?

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  1. 11 December, 11:41
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    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
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