= Pendulum clock
A <pendulum clock> uses a periodically swinging <simple pendulum> as its timekeeping element. For small <angular displacement>, an ideal <simple pendulum> of length $\ell$ has <period> $T\simeq2\pi\sqrt{\ell/g}$. This weak dependence on amplitude at small amplitude makes the <simple pendulum> useful for producing nearly equal time intervals.
Real <friction> would stop the swing. An <escapement> transfers small amounts of <energy> from a falling weight or wound spring while counting oscillations through a gear train. Changing the effective length changes the rate: increasing $\ell$ increases the <period> and makes the clock run slower. Temperature-dependent length and finite-amplitude corrections limit the ideal formula.
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