F=-kx+kx3/α2 where k and α are constants and k > 0. Determine U(x) and discuss the motion. What happens when E=kα2/4?
The Attempt at a Solution
The first part is easy.
U(x) = kx2/2-kx4/4α2
Now I'm looking for what happens when E=kα2/4
I know E=T+U, so T=kα2/4-kx2/2+kx4/4α2
To find T, I need to know velocity since T=1/2mv2
Solving for v, F=mv2d/dx, v=(k-3kx2/α2)/2(kx3/α2-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.