# Solving Differential - Equation of Motion

1. Jan 30, 2013

### aerowenn

Let's say I have the equation:

$\ddot {\theta}(t)(J + y(t)^2) + 2 \dot {\theta}(t) y(t) \dot y(t) + \ddot y(t)Jn$

It's the general form of an equation I'm working with to describe the motion of a beam. As you can see both ${\theta}(t)$ and y(t) are equations of t. J and Jn are just constants.

I'm wanting to solve for ${\theta}(t)$, $\dot {\theta}(t)$, and $\ddot {\theta}(t)$ as a function of time. These will correspond to position, velocity, and acceleration around an axis.

${\theta}(t)$ = (equation of t)

Any help would be greatly appreciated!

2. Jan 31, 2013

### Staff: Mentor

have you tried using e^iat style functions for theta(t)?

I ask because its sometimes used when you periodic motion which in your case is rotating about an axis.

3. Jan 31, 2013

### HallsofIvy

That's not a differential equation. Is one of those "+" signs supposed to be an "=" sign? Or is the whole formula equal to something, say "0"?

4. Jan 31, 2013

### aerowenn

Terribly sorry about that, you are correct. All of that is equal to 0.

As for the other response, I thought of that, but I'm not sure the general solution to second order differential equations applies here. Both functions are dependent on "t".