What law describes the relationship between force and spring compression or extension?

Hooke's Law is the principle that describes the relationship between the force applied to a spring and the resulting compression or extension of that spring. It states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position, provided the limit of elasticity is not exceeded. This means that if you compress or stretch a spring, the amount it compresses or stretches will increase as more force is applied, up to a certain limit.

For example, if you pull on a rubber band, the more you pull, the more it stretches; this linear relationship continues until the band reaches its elastic limit, beyond which it may deform permanently. This proportional relationship is mathematically expressed as F = kx, where F is the force applied, k is the spring constant (a measure of the spring's stiffness), and x is the displacement from its rest position. The clarity and mathematical precision of Hooke's Law make it critical in applications involving elastic materials and spring mechanics.