The force needed to extend or compress a spring by some distance is proportional to that distance.

More precisely, it describes the relationship between the force (F) applied to an elastic object, like a spring, and the resulting displacement (x) of that object.

Here's the mathematical representation:

* F = -kx

Where:

* F is the restoring force exerted by the spring (in Newtons)

* k is the spring constant (in Newtons per meter, N/m), which is a measure of the spring's stiffness

* x is the displacement from the spring's equilibrium position (in meters)

Important Notes:

* The negative sign indicates that the restoring force acts in the opposite direction of the displacement. This means the spring pulls back when stretched and pushes back when compressed.

* Hooke's Law applies only within the elastic limit of the spring. Beyond this limit, the spring will be permanently deformed and the relationship will no longer be linear.

* Hooke's Law is an idealization. Real springs exhibit some non-linear behavior, especially at large displacements.

Applications:

Hooke's Law has numerous applications in physics and engineering, including:

* Understanding the behavior of elastic materials

* Designing springs and other elastic components

* Modeling the vibrations of objects

* Analyzing the motion of simple harmonic oscillators

In essence, Hooke's Law provides a fundamental understanding of how elastic materials respond to forces and helps us predict their behavior.