I'm given the equation $\ddot s=s-s^3.$
I'm asked to compute the potential energy and sketch it. I'm also given $m=1.$ To do this I have done the following:
$$F=ma=\ddot s=s-s^3=\frac{-dV}{ds}=\frac{-d}{ds}\bigg(\frac{s^4}{4}-\frac{s^2}{2}\bigg).$$
So $V=\frac{s^4}{4}-\frac{s^2}{2}.$
So the total energy is $$E=\frac{1}{2}\dot s^2+\frac{s^4}{4}-\frac{s^2}{2}$$
How do I sketch this?