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Math Help - Don't get this pendelum problem??

  1. #1
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    Don't get this pendelum problem??



    how the heck do i find the equation?? i dont get it!! i just need help with the equation then i can do the rest
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  2. #2
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    Hello elpermic
    Quote Originally Posted by elpermic View Post

    how the heck do i find the equation?? i dont get it!! i just need help with the equation then i can do the rest
    d is a sinusoidal function of t; i.e. d = a + b\sin(ct+d), for some constants a, b, c, d

    d_{max}=110\Rightarrow 110 = a+b, since the maximum value of the sine function is 1

    d_{min}=50 =a-b, since the minimum value of the sine function is -1

    \Rightarrow a=80, b= 30

    So d = 80+30\sin(ct+d)

    \sin(ct+d) has period \frac{2\pi}{c}\Rightarrow \frac{2\pi}{c}= 6, since the pendulum performs one complete swing in 6 seconds

    \Rightarrow c = \frac{\pi}{3}

    And d = 110 when t = 1.3\Rightarrow \sin\Big(\frac{1.3\pi}{3}+d\Big) = 1

    \Rightarrow \frac{1.3\pi}{3}+d = \frac{\pi}{2}

    \Rightarrow d = \pi\Big(\frac{1}{2}-\frac{13}{30}\Big)=\frac{\pi}{15}

    \Rightarrow d =80+30\sin\Big(\frac{\pi t}{3}+\frac{\pi}{15}\Big)

    Grandad
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