At a certain harbor, the tides cause the ocean surface to rise and fall a distance...

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At a certain harbor, the tides cause the ocean surface to rise and fall a distance...

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

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Answer 1

Answer #1

amplitude will be d/2.

starting from highest level then equation of SHM will be

y = A cos(wt)

w = 2pi/T = 2pi/(11.7 hr)

y = (d/2) cos(2 pi t / 11.7)

putting y = 0.250d

0.250d = 0.500d cos(2pi t / 11.7)

cos(2 pi t / 11.7) = 0.5

2 pi t / 11.7 = pi/3

t = 11.7 / (2 x 3) = 1.95 h

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Answer 2

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At a certain harbor, the tides cause the ocean surface to rise and fall a distance...

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