# second order ODE with sin term

• Dec 8th 2009, 08:46 AM
robotENGR
second order ODE with sin term
i am trying to solve this ode but can't seem to get any traction:

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

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

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

MT

(This is a derivitive of a nasty case where: $\displaystyle \frac {d^2 \theta(\tau)} {d \tau^2} + \sin(\theta_{s} + \theta(\tau) ) = 0$ which I still don't know how to solve with the same B.C)
• Dec 8th 2009, 09:08 AM
TheEmptySet
Quote:

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

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

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

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

MT

(This is a derivitive of a nasty case where: $\displaystyle \frac {d^2 \theta(\tau)} {d \tau^2} + \sin(\theta_{s} + \theta(\tau) ) = 0$ 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)