In simple harmonic motion, when is the potential energy at its maximum?

In simple harmonic motion (SHM), potential energy is maximized when the object is at the extreme positions of its motion, which correspond to the amplitude points. At these positions, the displacement from the equilibrium position is greatest. When the object is at the amplitude, it is momentarily at rest, and all the energy in the system is stored as potential energy.

Conversely, at the equilibrium position, the potential energy is at a minimum because the object has its maximum kinetic energy and is moving quickly through that point. At half the amplitude, the potential energy is also not at its maximum, as it is less than what is observed at the extreme points. Thus, the correct answer reflects that potential energy is highest exclusively at the maximum displacement, which occurs at the amplitude positions.