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Math Help - second order ODE with sin term

  1. #1
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    second order ODE with sin term

    i am trying to solve this ode but can't seem to get any traction:

    \frac {d^2 \theta(\tau)}  {d \tau^2} + \sin(\theta(\tau) ) = 0

    \theta(0) = A
    \dot{\theta}(0) = 0

    How would i go about solving this?
    Thank you very much!!

    MT

    (This is a derivitive of a nasty case where: \frac {d^2 \theta(\tau)}  {d \tau^2} + \sin(\theta_{s} + \theta(\tau) ) = 0 which I still don't know how to solve with the same B.C)
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  2. #2
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    Quote Originally Posted by robotENGR View Post
    i am trying to solve this ode but can't seem to get any traction:

    \frac {d^2 \theta(\tau)} {d \tau^2} + \sin(\theta(\tau) ) = 0

    \theta(0) = A
    \dot{\theta}(0) = 0

    How would i go about solving this?
    Thank you very much!!

    MT

    (This is a derivitive of a nasty case where: \frac {d^2 \theta(\tau)} {d \tau^2} + \sin(\theta_{s} + \theta(\tau) ) = 0 which I still don't know how to solve with the same B.C)

    The solution involves elliptic integrals

    Here is a link to a wiki with derivation

    http://en.wikipedia.org/wiki/Pendulum_(mathematics)
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