# Homework Help: Potential well, harmonic oscillator

1. Dec 4, 2013

### skate_nerd

1. The problem statement, all variables and given/known data
Parabolic harmonic oscillator potential well. A particle is trapped in the well, oscillating classically back and forth between x=b and x=-b. The potential jumps from Vo to zero at x=a and x=-a. The particle's energy is Vo/2. I need to find the potential function V(x) in terms of Vo and a.

2. Relevant equations
E=K+V=.5mv2+.5Cx2=Vo/2

3. The attempt at a solution
Honestly I am really stumped. I tried several approaches, and I think I might just be making this way harder than it should be. I just imagine when dealing with a classical oscillating in a parabolic potential well, you should just use the equation i put in the relevant equations section, and then solve for V(x). However that isn't a function of x, its a function of velocity. Also it is lacking the required dependence on a. I have no idea how a could come into the equation for V(x). I tried thinking of a bunch of conditions to apply it but nothing made sense. Any guidance would be awesome