#vibration

Single-degree-of-freedom vibration (spring-mass-damper) maths as an API, computed locally and deterministically. The natural endpoint gives the undamped natural frequency of a spring-mass system, ωn = √(k/m), fn = ωn/2π and the period T = 1/fn, and solves for whichever of the stiffness, mass or natural frequency you leave out. The damped endpoint analyses a damped system from the stiffness, mass and either a damping coefficient or a damping ratio: it returns the critical damping coefficient cc = 2√(km), the damping ratio ζ = c/cc, the classification (underdamped, critically damped or overdamped), and — for an underdamped system — the damped natural frequency ωd = ωn·√(1−ζ²), its period, and the logarithmic decrement δ = 2πζ/√(1−ζ²). The pendulum endpoint gives the period and frequency of a simple pendulum, T = 2π·√(L/g), and solves the length from a target period, with gravity adjustable. Everything is computed locally and deterministically, so it is instant and private. Ideal for mechanical, structural and earthquake-engineering tools, machine-condition-monitoring and isolation-design apps, instrument and clock design, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is discrete spring-mass-damper vibration; for standing waves on strings and in air columns use a standing-wave API.

api.oanor.com/vibration-api