Balance & Hairspring: the Regulating Organ

A torsional pendulum: its natural period decides the rate

$T = 2\pi\sqrt{I/k}$

Moment of inertia I 1.00× Hairspring stiffness k 1.00× Amplitude A 270° Slow-motion 0.08×

Stiffer spring or lighter wheel → faster beat. Amplitude barely changes the period (isochronism).