Ah thanks, that should be great help.
You can view the assignment here http://www.maths.utas.edu.au/People/Forbes/KYA314Ass2in2011.pdf . Question 2. (a) is the one in question. I think I've typed it correctly though.
Edit: I have confirmed it is not a typo.
I just checked, it's definitely \frac{1}{2}x^{2}+V(x)=E. I did have to fix the V(X) and the domain of the integration.
You're saying do this?
\int f(x) dx = \int \frac{\partial^{2}x}{\partial t^{2}} dx
\int \frac{\partial^{2}x}{\partial t^{2}} dx = \int \frac{\partial}{\partial t} (...
Homework Statement
Consider a mechanical system describe by the conservative 2nd-order ODE
\frac{\partial^{2}x}{\partial t^{2}}=f(x)
(which could be non linear). If the potential energy is V(x)=-\int^{x}_{0} f(\xi) d \xi, show that the system satisfies conservation of energy...