What happens at the extremes of motion in SHM?

At the extremes of motion in Simple Harmonic Motion (SHM), the velocity is zero and potential energy is at its maximum.

In Simple Harmonic Motion (SHM), the motion of the object is sinusoidal in time and demonstrates a single resonant frequency. The extremes of motion, also known as the amplitude, are the furthest points from the equilibrium position that the object reaches. At these points, the object momentarily comes to rest before reversing its direction of motion. This is because the velocity of the object is zero at the extremes of motion.

The potential energy of the object is also at its maximum at the extremes of motion. This is due to the fact that potential energy and kinetic energy are inversely related in SHM. When the object is at the equilibrium position, its velocity is at its maximum, meaning its kinetic energy is also at its maximum. Conversely, when the object is at the extremes of motion, its velocity (and therefore its kinetic energy) is zero, meaning its potential energy is at its maximum.

The relationship between velocity, potential energy, and position in SHM is a fundamental aspect of the motion. It's important to understand that the velocity and potential energy of the object are constantly changing as the object moves back and forth. However, the total energy of the system (the sum of the kinetic and potential energy) remains constant. This is a direct consequence of the conservation of energy principle.

In summary, at the extremes of motion in SHM, the object momentarily comes to a stop and its potential energy reaches a maximum. This is a direct result of the sinusoidal nature of the motion and the conservation of energy principle. Understanding these concepts is crucial for a deep understanding of SHM and its applications in physics.