# How is simple harmonic motion related to Hooke law?

##### 1 Answer

A particle is said to be in *simple harmonic motion* if it satisfies the following differential equation:

where

Hooke's law is a model for the behavior of ellastic materials, such as a spring (and is only valid if the material does not suffer strong deformations). It states that the magnitude of the force *restoring force*, that is, it's direction is opposite to the direction of the displacement vector:

Newton's second law states that the force

This two equations give us the relation

Rearranging, we get:

Divind by the mass

Associating the

Therefore, any system that satisfies Hooke's law and isn't acted upon by any other forces is in simple harmonic motion.