In simple harmonic motion, what is the relationship between force and displacement?

In simple harmonic motion (SHM), the relationship between force and displacement is characterized by Hooke's Law, which states that the restoring force acting on an object is directly proportional to the displacement from its equilibrium position. This force acts in the opposite direction to the displacement, meaning that when an object is displaced to one side, the restoring force pulls it back toward the equilibrium position.

The key feature of this relationship is that the further the object is from equilibrium (the greater the displacement), the stronger the restoring force working to bring it back, which leads to oscillatory motion. This dynamic is fundamentally what allows systems such as springs and pendulums to exhibit periodic behavior. When the displacement is zero (equilibrium position), the restoring force is also zero, and as the object moves away from this position, the force increases in the opposite direction.

This understanding of force and displacement in SHM is crucial in predicting the motion of oscillating systems and is the basis for many applications in physics and engineering.