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Thread: function question

  1. #1
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    function question

    thanks skeeter
    Last edited by captain_jonno; Oct 9th 2009 at 07:07 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; Oct 8th 2009 at 07:42 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

    $\displaystyle
    y = A\cos(\omega t + \delta)
    $

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

    $\displaystyle
    \omega = \frac{\pi}{15}
    $

    $\displaystyle
    A = -5.2
    $

    at this point ...

    $\displaystyle
    y = -5.2\cos\left(\frac{\pi}{15} t + \delta\right)
    $

    at $\displaystyle t = 0$ , $\displaystyle y = -2.6$

    $\displaystyle
    -2.6 = -5.2\cos\left(\frac{\pi}{15} (0) + \delta\right)
    $

    $\displaystyle
    \frac{1}{2} = \cos\left(\delta\right)
    $

    $\displaystyle
    \delta = \frac{\pi}{3}
    $

    so ...

    $\displaystyle
    y = -5.2\cos\left(\frac{\pi}{15} t + \frac{\pi}{3}\right)
    $

    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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