What force from a stretched spring is often modeled by Hooke's law?

What force from a stretched spring is often modeled by Hooke's law? A stretched spring exerts a restoring force, modeled for small deformations by Hooke's law.

For an ideal linear spring, the restoring force is written F = −kx. The spring constant k measures stiffness, x is displacement from equilibrium, and the minus sign shows that the force points opposite the displacement. Stretching pulls the spring back; compressing pushes it outward toward its relaxed length.

Hooke's law is an approximation, not a universal rule. Real springs follow it only over a suitable elastic range. Beyond the proportional limit, a spring may deform permanently, buckle, or otherwise depart from the straight-line relationship between force and displacement.

Robert Hooke first announced the relationship in 1676 through a Latin anagram and published its solution in 1678: “ut tensio, sic vis,” meaning “as the extension, so the force.” The law also underlies spring scales, mechanical clocks, and many vibration models.