Energy diagrams are important to understand the dynamics of a system. The topology of an energy diagram helps illustrate the equilibrium points of the system.
The point in the energy diagram at which the system’s potential energy is the lowest is known as the local minima. The system tends to stay in this position indefinitely unless acted upon by a net force. The slope of the potential energy diagram at the local minima is zero, indicating that zero net force is acting on the system. The slope is positive on either side of the minima, which suggests that the net force acting upon the system is a restoring one. Similarly, the net force acting on the system at the local maxima is also zero, but this is an unstable equilibrium point. Any movement away from this point results in a force that is acting away from the point.
There will always be a neutral equilibrium point characterized by the constant potential energy regime of the potential energy diagram, where the net force on the system will be zero. Any movement on either side of the neutral equilibrium position will result in a net force on the system, neither restoring nor disrupting.
This text is adapted from Openstax, University Physics Volume 1, Section 8.4: Potential Energy Diagrams and Stability.
