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

Tags:
1. Dec 12, 2016

### Robin64

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. Dec 12, 2016

### Hiranya Pasan

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