How do Newton's laws apply to harmonic motion?

Newton's laws apply to harmonic motion by explaining the forces acting on an oscillating object.

Harmonic motion is the repetitive motion of an object about an equilibrium position. Newton's first law states that an object at rest will remain at rest, and an object in motion will remain in motion at a constant velocity, unless acted upon by an external force. In the case of harmonic motion, the external force is the restoring force, which brings the object back to its equilibrium position. This force is proportional to the displacement from the equilibrium position, as described by Hooke's law.

Newton's second law states that the acceleration of an object is directly proportional to the net force acting on it, and inversely proportional to its mass. In the case of harmonic motion, the acceleration is also proportional to the displacement from the equilibrium position, as described by the equation of motion for simple harmonic motion. This equation relates the acceleration, displacement, and frequency of the oscillation.

Newton's third law states that for every action, there is an equal and opposite reaction. In the case of harmonic motion, this means that the restoring force is equal and opposite to the force causing the displacement. For example, in a mass-spring system, the force exerted by the spring on the mass is equal and opposite to the force exerted by the mass on the spring.

Overall, Newton's laws provide a framework for understanding the forces and motion involved in harmonic motion. By applying these laws, we can analyse and predict the behaviour of oscillating systems.