Potential energy, equilibrium and turning points

When a body moves in one dimension under conservative forces (spring, gravity), its potential energy $E_\text{pot}(x)$ is a function of position. The graph of this function is extremely powerful: the minimum is the point of equilibrium, the intersections with $E_\text{tot}$ are the turning points, and for a parabola the motion is harmonic with a calculable period.

• The potential-energy parabola
• Period of small oscillations