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    (Original post by Gome44)
    While the normal pendulum equation is solvable with elliptic integrals, the quadratically damped pendulum is not unfortunately.

    Only numerical methods can be used to evaluate t at certain theta (incidentally I took this from one of my Matlab projects)
    Oh :0

    My bad. I used Runge-Kutta for both in my program anyway.
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    (Original post by Gome44)
    You have the differential equation below. Prove the thing next to that. I can't do it so don't ask me for help, have fun xx

    Edit: I now know how to do it. Alas, I still will not help to be evil
    This is fun. Let's see if we can get started. First of all, let y = \dot_{\theta}. Then we're going to look at

    \displaystyle \frac{d}{d\theta}(y^2) = \frac{1}{\dot{\theta}} \frac{d}{dt}(\dot{\theta}^2)

    If you crunch through this for a bit, you'll get something like

    \displaystyle \frac{d}{d\theta}(y^2) = -y^2 -2\sin \theta

    which looks not too unpleasant. Who wants to take it up from here?
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    (Original post by Gregorius)
    This is fun. Let's see if we can get started. First of all, let y = \dot_{\theta}. Then we're going to look at

    \displaystyle \frac{d}{d\theta}(y^2) = \frac{1}{\dot{\theta}} \frac{d}{dt}(\dot{\theta}^2)

    If you crunch through this for a bit, you'll get something like

    \displaystyle \frac{d}{d\theta}(y^2) = -y^2 -2\sin \theta

    which looks not too unpleasant. Who wants to take it up from here?
    This is a really good idea. That's why I made it in post 4

    But on a more serious note: what are the initial conditions?
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    (Original post by Gome44)
    Not the way I've been told to do it, but it looks like that would work
    What was your method?
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    (Original post by atsruser)
    What was your method?
    Actually I've just tried my method and it is essentially the same, just a different substitution (v= exp(-theta/2)w where v=d(theta)/dt).
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    (Original post by atsruser)
    This is a really good idea. That's why I made it in post 4
    Doh! Sorry.
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    (Original post by Gregorius)
    Doh! Sorry.
    I was hiding my light under a spoiler-shaped bushel which is why you missed my display of calculus-related brilliance, I guess.
 
 
 
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