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Math Help - function question

  1. #1
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    function question

    thanks skeeter
    Last edited by captain_jonno; October 9th 2009 at 08:07 AM.
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  2. #2
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    Quote Originally Posted by captain_jonno View Post
    A boat is hit by a wave and oscillates 5.2 deg on either side of upright. If the ship is leaning 2.6 deg to the left and moving toward upright at t=0, write a function describing the lean angle, theta, as a function of time. Period of boats roll is 30sec.
    see attached graph ...
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  3. #3
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    hey skeeter i dont actually need the graph, but the working out to get to that point. If you know how?

    plus when i plug that equation into my ti-83 the graph doesnt look the same.

    your using a mac program for that right?
    Last edited by mr fantastic; October 8th 2009 at 08:42 PM. Reason: Merged posts
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  4. #4
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    my mistake ... I misread the 5.2 degrees "either side" as the total oscillation.

    General form for the equation that models this motion will be

     <br />
y = A\cos(\omega t + \delta)<br />

    period = T = 30 \, sec \, = \frac{2\pi}{\omega}

     <br />
\omega = \frac{\pi}{15}<br />

     <br />
A = -5.2<br />

    at this point ...

     <br />
y = -5.2\cos\left(\frac{\pi}{15} t + \delta\right)<br />

    at t = 0 , y = -2.6

     <br />
-2.6 = -5.2\cos\left(\frac{\pi}{15} (0) + \delta\right)<br />

     <br />
\frac{1}{2} = \cos\left(\delta\right)<br />

     <br />
\delta = \frac{\pi}{3}<br />

    so ...

     <br />
y = -5.2\cos\left(\frac{\pi}{15} t + \frac{\pi}{3}\right)<br />

    make sure your calculator is in radian mode when you graph it.
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  5. #5
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    Quote Originally Posted by captain_jonno View Post
    Hi chaps & chapettes,
    What about us chapeaus?
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