Hooke's Law

Hooke's law states that the force needed to extend or compress a spring or other elastic object by some distance is directly proportional to that distance, within the material's elastic limit. English scientist Robert Hooke first announced the relationship in 1660 as an anagram, ceiiinosssttuv, publishing its solution in 1678 as the Latin phrase ut tensio, sic vis, meaning as the extension, so the force. The law is commonly written as F equals negative k times x, where F is the restoring force, x is the displacement from the object's equilibrium position, and k is a constant, called the spring constant, characteristic of the particular elastic object. Hooke's law holds only approximately, breaking down once a material is stretched or compressed beyond its elastic limit, past which it deforms permanently rather than returning to its original shape, and it remains foundational to the study of elasticity in materials science and engineering and to the mathematics of simple harmonic motion for any system whose restoring force is proportional to displacement.