Orbital Potential Energy to find r and phi in terms of t.

[10Exahertz]

Homework Statement

A particle in central force field has the orbit r=cφ^2, c is a constant. Find the potential energy, Find r and phi in terms of t.
I get how to find the potential energy and found it to be U=-l^2/mu (2c/r^3+l/2r^2)
l is angular momentum and mu is the reduced mass
But how do I get r and phi in terms of t after this?

Homework Equations

From what my professor showed in class l=mu r^2 dφ/dt was important
he used that to integrate and get r^2(t)=lt/mu
I'm trying to use this method to get r and phi

Any help is much appreciated, thanks!

 

[mfb]

I'm trying to use this method to get r and phi

Sounds good. Once you have dφ/dt, you can get dt/dφ and integrate.