Isotropic Harmonic Oscillator Orbit Calculation | Central Motion Problem

[fightonfire59]

Homework Statement

Consider an isotropic harmonic oscillator whose potential is given by V(r)=0.5kr^2. Calculate the value of r(t) for the orbit of a particle.

Homework Equations

dr/dt=$$\sqrt{2/m(E-0.5kr^2-L^2/2mr^2)}$$ (call the right side of the eqn 'stuff')

The Attempt at a Solution

I'm unable to solve the integral $$\int$$$$\frac{dr}{stuff}$$ as is.
I'm sure there's a subsitution or some other trick I can do to make the integral solvable but I can't figure it out =/

 

[diazona]

Note that when you separate the equation, you'll get a fraction within a fraction:
$$\frac{\mathrm{d}r}{\sqrt{\cdots + A/r^2}} = \cdots$$
It's usually a good idea to simplify such expressions like so:
$$\frac{\mathrm{d}r}{\sqrt{\frac{1}{r^2}(\cdots + A)}} = \cdots$$
so that you're left with a regular polynomial times some overall factor. With a couple more steps, you can get that into a form where you can use the substitution $u = r^2$.