- #1

- 7

- 4

## Homework Statement

F=-kx+kx

^{3}/α

^{2}where k and α are constants and k > 0. Determine U(x) and discuss the motion. What happens when E=kα

^{2}/4?

## Homework Equations

F=ma=mv

^{2}d/dx

U=-∫Fdx

## The Attempt at a Solution

The first part is easy.

U(x) = kx

^{2}/2-kx

^{4}/4α

^{2}

Now I'm looking for what happens when E=kα

^{2}/4

I know E=T+U, so T=kα

^{2}/4-kx

^{2}/2+kx

^{4}/4α

^{2}

To find T, I need to know velocity since T=1/2mv

^{2}

Solving for v, F=mv

^{2}d/dx, v=(k-3kx

^{2}/α

^{2})/2(kx

^{3}/α

^{2}-kx)

^{3/2}

Here's where I'm not sure I'm going in the right direction. If I find T, I introduce an m term. The potential energy is independent of mass, so why would kinetic energy depend on mass? It also seems as though the whole thing is independent of time.