#spring

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.

api.oanor.com/hooke-api

Helical compression-spring maths as an API, computed locally and deterministically. The rate endpoint computes the spring rate from the wire diameter, the mean coil diameter and the number of active coils using k = G·d⁴/(8·D³·n), where the shear modulus G is taken from the material (music wire and spring steel, stainless, phosphor bronze, beryllium copper, titanium and more) or supplied directly — and it reports the rate in newtons per millimetre, newtons per metre and pounds per inch, along with the spring index C = D/d. The force endpoint relates force and deflection through F = k·x in both directions, taking the rate directly or deriving it from the geometry. The stress endpoint computes the shear stress in the wire, τ = 8·F·D·Kw/(π·d³), applying the Wahl correction factor Kw = (4C−1)/(4C−4) + 0.615/C for curvature and direct shear, and also reports the uncorrected stress. Lengths are in millimetres, force in newtons and stress in megapascals. Everything is computed locally and deterministically, so it is instant and private. A design aid — keep the spring index between about 4 and 12 and confirm against the material's allowable stress. Ideal for mechanical-design and CAD tools, spring-selection and prototyping apps, maker and robotics projects, and engineering calculators. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is helical-spring design; for beam deflection use a beam API.

api.oanor.com/springcoil-api