Potential Energy of various systems

The graphical representation of the one-dimensional constrained potential energy function U(x) for an object. Also shown are various values of the total mechanical energy. Points (A, B, C, D) on the potential-energy versus position graph with zero slope are equilibrium positions. The equilibrium is characterized as stable (A), unstable (B), or neutral (D), according to the graph in the neighborhood of the equilibrium point. For a curve like that near point C the equilibrium cannot be characterized simply as stable, unstable, or neutral. A plot of U versus x for a system that has a position of unstable equilibrium, located at x=0. In this case, the force of the system for finite displacements is directed away from x=0.