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I 2nd order differential equation problem with sin(theta)

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  1. Dec 12, 2016 #1
    I have a differential equation that is essentially this: θ''(t)=c*sin[θ(t)] . I've been stymied trying to find a solution, and even when I tried using Maple, I got a nasty integral of a Jacobian amplitude. I'm tempted to use a small angle approximation, but the angle is 0≤θ≤π/2. I know this is similar to a pendulum, but it is not a pendulum (I'm modeling the the behavior of a catapult as a function of time). Any suggestions?
     
  2. jcsd
  3. Dec 12, 2016 #2
    θ''(t)=dθ'/dt=c sinθ, use the chain rule to change the variables dθ'/dt=(dθ'/dθ)*(dθ/dt)=(dθ'/dθ)*θ' now sub. to the differential equation => θ'(dθ'/dθ)=c sinθ now it has been converted to separable differential equation.
    <Mod note: Post edited to remove full solution>
     
    Last edited by a moderator: Dec 13, 2016
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