How is the restoring force related to displacement in simple harmonic motion?

The restoring force in simple harmonic motion is directly proportional to displacement.

In simple harmonic motion, an object oscillates back and forth around an equilibrium position due to a restoring force. This restoring force is always directed towards the equilibrium position and is directly proportional to the displacement from that position. This means that the further the object is from its equilibrium position, the stronger the restoring force will be.

The relationship between the restoring force and displacement can be described by Hooke's law, which states that the force exerted by a spring is directly proportional to the amount it is stretched or compressed. This law applies to any system that exhibits simple harmonic motion, including pendulums and mass-spring systems.

The equation that describes the relationship between the restoring force and displacement is F = -kx, where F is the restoring force, k is the spring constant (a measure of the stiffness of the spring), and x is the displacement from the equilibrium position. The negative sign indicates that the force is always directed towards the equilibrium position.

Understanding the relationship between the restoring force and displacement is important for understanding the behaviour of systems that exhibit simple harmonic motion. It allows us to predict the motion of the object and calculate important quantities such as the period and frequency of the oscillation.