At a certain harbor, the tides cause the ocean surface to riseand fall a distanc

Question

At a certain harbor, the tides cause the ocean surface to riseand fall a distance d (from highest level to lowest level)in simple harmonic motion, with a period of 12.0 h. How long (inhours) does it take for the water to fall a distance d/4from its highest level? Is d/4 the displacement? Should I use the formulax=xmcos(t+)? What steps do I need to follow?Please help? At a certain harbor, the tides cause the ocean surface to riseand fall a distance d (from highest level to lowest level)in simple harmonic motion, with a period of 12.0 h. How long (inhours) does it take for the water to fall a distance d/4from its highest level? Is d/4 the displacement? Should I use the formulax=xmcos(t+)? What steps do I need to follow?Please help?

Explanation / Answer

we know x=xmcos(t+) where x = displacement = d / 4           xm = amplitude = d / 2   Since thedistance from highest to lowest level is d          =initial phase = 0 substitue we get   ( d/ 4 ) = ( d / 2 ) cos (t + 0 )                             0.5 = cos t                           t = / 3   rad                 ( 2 / T ) t = / 3                                t = T / 6 where T = time period = 12 h So, t = 2 h

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