Hooke's Law and the Spring Constant

Named after Robert Hooke (1678), Hooke's law states that within its elastic limit, a spring's restoring force is proportional to its displacement: F = −k·x. The spring constant k is the ratio F/x — the force in newtons needed to stretch or compress the spring by one meter.

Stored Elastic Energy

Stretching a spring does work against the growing restoring force, storing energy as elastic potential energy: E = ½kx². Because the energy scales with the square of the displacement, doubling the stretch quadruples the stored energy — the reason springs are powerful energy reservoirs in mechanical systems.

Springs in Motion

Attach a mass to the spring and it oscillates with frequency f = (1/2π)·√(k/m). This simple harmonic motion underlies suspension systems, seismographs, tuning forks, and the balance wheels of mechanical watches — a spring and mass are a clock all by themselves.