Hooke's Law & Spring API

Hooke's law and elastic potential energy as an API, computed locally and deterministically. The hooke endpoint applies F = k·x — the restoring force of a spring equals its spring constant times the extension — and solves for whichever of the force, the spring constant or the displacement you leave out, also returning the elastic potential energy ½·k·x². The energy endpoint computes the elastic potential energy E = ½·k·x² stored in a stretched or compressed spring, solves the extension from a stored energy, and finds the work done in stretching a spring from one extension to another, W = ½·k·(x2² − x1²). The combine endpoint combines springs: in series the assembly is softer, 1/k = Σ 1/kᵢ, and in parallel it is stiffer, k = Σ kᵢ — the spring equivalent of resistors in a circuit. Everything is computed locally and deterministically, so it is instant and private. Ideal for physics and mechanics-education tools, spring and suspension design, mechanism and gadget engineering, and simulation software. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is the force-extension law and elastic energy; for the spring rate of a helical coil from its geometry use a spring-coil API and for spring-mass natural frequency use a vibration API.