butterflydreamer
  • butterflydreamer
SIMPLE HARMONIC MOTION QUESTION - Please help me LOL. I completely forgot how to solve these types of questions :( A ship needs 10m of water to pass down a channel safely. At low tide, the channel is 9m deep and at high tide it is 12m deep. Low tide is at 10 a.m and high tide at 5pm. Assume that the tidal motion is simple harmonic. period= 14hrs and amplitude = 1.5m **At what time can the ship safely proceed before midnight?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
:)
anonymous
  • anonymous
For the first two qs show that the 2nd derivative = -w^2 x differentiate twice n then manipulate to get into that form
butterflydreamer
  • butterflydreamer
Would this be the equation to use? \[x = 1.5 \cos (\frac{ \pi }{ 7 } + \alpha) + 10.5\] Then let t = 0 , x = 9 so... \[9 = 10.5 + 1.5\cos \alpha\] \[-1.5 = 1.5 \cos \alpha\] \[\cos \alpha = -1\] \[\alpha = \pi\] let x = 10 (because.. the ship needs 10m of water?) \[10 = 1.5 \cos (\pi t /7 + \pi) + 10.5\] \[-0.5 = 1.5 \cos (\pi t/7 + \pi) \] \[-\frac{ 1 }{ 3} = \cos (\pi t/7 + \pi) \] \[\cos ^{-1} (-1/3) = \frac{ \pi t }{ 7 } + \pi \]

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butterflydreamer
  • butterflydreamer
\[\cos ^{-1}(\frac{ 1 }{ 3 }) + \pi = \frac{ \pi t }{ 7 } + \pi\] \[\frac{ \pi t }{ 7 } = \cos ^{-1} (\frac{ 1 }{ 3 }) \] \[t = \frac{ 7\cos ^{-1}(\frac{ 1 }{ 3 }) }{ \pi }\]
butterflydreamer
  • butterflydreamer
right? xD going out on a limb right now.
butterflydreamer
  • butterflydreamer
so my final answer is 12:45 pm and 9:15 pm but it doesn't feel correct :/
butterflydreamer
  • butterflydreamer
*** 12:44pm and 9:15 am
dan815
  • dan815
|dw:1436575570798:dw|
dan815
  • dan815
|dw:1436576262945:dw|
butterflydreamer
  • butterflydreamer
thanksss ^_^

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