A mass attached to a spring experiences a restoring force F = -k·x proportional to its displacement from equilibrium. Because the force always points back toward equilibrium, the mass oscillates forever (in the ideal frictionless case) with a fixed frequency that depends only on the spring constant k and the mass m.
Simple harmonic motion parametersAngular frequency ω = √(k / m)
Period T = 2π √(m / k)
Frequency f = 1 / T
Position x(t) = A · cos(ωt + φ)
The independent variable
Notice the period depends only on k and m, not on the amplitude A. A gentle push and a hard push both produce the same ticking rate — this is why a mass-spring clock is a reliable timekeeper.