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Math Help - Length of pendulum

  1. #1
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    Length of pendulum

    the motion of a pendulum can be modelled by the function x(t)=10cos(2t)*0.95^t, where x is the horizontal displacement from the rest position, in centimetres, as a function of time, t, in seconds
    Determine the length of the pendulum.

    answer is 245 cm in the book, i want to know the steps, thanks
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  2. #2
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    Quote Originally Posted by yoman360 View Post
    the motion of a pendulum can be modelled by the function x(t)=10cos(2t)*0.95^t, where x is the horizontal displacement from the rest position, in centimetres, as a function of time, t, in seconds
    Determine the length of the pendulum.

    answer is 245 cm in the book, i want to know the steps, thanks
    period of a pendulum, T = 2\pi\sqrt{\frac{L}{g}}

    solve for L ...

    L = \frac{gT^2}{4\pi^2}<br />


    T = \frac{2\pi}{2}= \pi

    g = 980 \, cm/s^2

    calculate the value of L
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  3. #3
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    Quote Originally Posted by skeeter View Post
    period of a pendulum, T = 2\pi\sqrt{\frac{L}{g}}

    solve for L ...

    L = \frac{gT^2}{4\pi^2}<br />


    T = \frac{2\pi}{2}= \pi

    g = 980 \, cm/s^2

    calculate the value of L
    How do I find the length using x(t)=10cos(2t)*0.95^t ???
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  4. #4
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    Quote Originally Posted by yoman360 View Post
    How do I find the length using x(t)=10cos(2t)*0.95^t ???
    the only piece of information you can determine from the given position equation is the period of oscillation.
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  5. #5
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    Quote Originally Posted by skeeter View Post
    the only piece of information you can determine from the given position equation is the period of oscillation.
    so basically x(t)=10cos(2t)*0.95^t is pointless info
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  6. #6
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    Quote Originally Posted by yoman360 View Post
    so basically x(t)=10cos(2t)*0.95^t is pointless info
    not pointless ... but you cannot determine the length of the pendulum without the necessary equations of simple harmonic motion from physics.
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