What's the role of equilibrium in SHM?

In Simple Harmonic Motion (SHM), equilibrium plays the role of the midpoint where the restoring force is zero.

In the context of Simple Harmonic Motion, equilibrium is a crucial concept. It refers to the position where the net force acting on the object is zero. This is typically the midpoint of the motion, where the object is neither being stretched nor compressed. In other words, it's the point where the object would stay if it were not disturbed.

The role of equilibrium in SHM is closely tied to the concept of restoring force. The restoring force is the force that brings the object back towards equilibrium whenever it is displaced. This force is directly proportional to the displacement from the equilibrium position and acts in the opposite direction. This relationship is often described by Hooke's Law, which states that the force exerted by a spring is equal to the spring constant times the displacement from the equilibrium position.

In SHM, the object oscillates about the equilibrium position. When the object is at the equilibrium position, the velocity is at its maximum and the acceleration is zero because there is no restoring force acting on it. As the object moves away from the equilibrium position, the restoring force increases, causing the object to decelerate until it reaches the maximum displacement, where the velocity is zero and the acceleration is at its maximum. Then, the restoring force causes the object to accelerate back towards the equilibrium position, completing one cycle of the motion.

The equilibrium position is also important in determining the potential energy of the system in SHM. The potential energy is at its minimum at the equilibrium position because the object is neither stretched nor compressed. As the object moves away from the equilibrium position, the potential energy increases, reaching its maximum at the maximum displacement.

In conclusion, the equilibrium position in SHM is the point where the restoring force is zero, and it serves as the reference point for the motion, the restoring force, and the potential energy of the system.