The restoring force in simple harmonic motion is directly proportional to the displacement from the equilibrium position.

In simple harmonic motion, an object oscillates back and forth around a central equilibrium position due to a restoring force. This force is always directed toward the equilibrium position and is directly proportional to the displacement from that position. Consequently, the greater the distance of the object from the equilibrium position, the stronger the restoring force acting on it.

This relationship between the restoring force and displacement is articulated by Hooke’s Law, which states that the force exerted by a spring is directly proportional to the amount it is stretched or compressed. Hooke’s Law is applicable to any system that demonstrates simple harmonic motion, including pendulums and mass-spring systems.

The mathematical representation of this relationship is given by the equation:

In this equation, $F$ represents the restoring force, $k$ is the spring constant (a parameter that quantifies the stiffness of the spring), and $x$ denotes the displacement from the equilibrium position. The negative sign indicates that the force acts in the opposite direction of the displacement, always pulling the object back toward the equilibrium position.

Grasping the connection between the restoring force and displacement is crucial for understanding the behavior of systems exhibiting simple harmonic motion. This understanding enables us to predict the motion of the object and calculate significant quantities such as the period and frequency of the oscillation.