How Do You Determine U(x) for a Particle Under a Nonlinear Force?

[eku_girl83]

A particle is under the influece of a force F=-kx+kx^3/(a^2), where k and a are constants and k is positive. Determine U(x) and discuss the motion. What happens when E=1/4 (k a^2)?

I know F = - grad U, but how do I use this fact to set up the problem?
Can someone help me to get started?

Thanks!

 

[Galileo]

This is a one-dimensional problem, so no need for gradients. Just F=-dU/dx

So start by finding (a) U(x).

 

[Gokul43201]

A particle is under the influece of a force F=-kx+kx^3/(a^2), where k and a are constants and k is positive. Determine U(x) and discuss the motion. What happens when E=1/4 (k a^2)?
I know F = - grad U

In one-dimension, that's F(x) = -dU(x)/dx. Now what can you do to express U(x) in terms of F(x) ?

Edit : Started before Galileo's post was up...now redundant as it's saying the same thing.