simplegravity

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Gravity-swing pendulum[edit]

Schoolhouse regulator style pendulum wall clock

The pendulum swings with a period that varies with the square root of its effective length. For small swings the period T, the time for one complete cycle (two swings), is

${\displaystyle T=2\pi {\sqrt {\frac {L}{g}}}\,}$

where L is the length of the pendulum and g is the local acceleration of gravity. All pendulum clocks have a means of adjusting the rate. This is usually an adjustment nut under the pendulum bob which moves the bob up or down on its rod. Moving the bob up reduces the length of the pendulum, reducing the pendulum's period so the clock gains time. In some pendulum clocks, fine adjustment is done with an auxiliary adjustment, which may be a small weight that is moved up or down the pendulum rod. In some master clocks and tower clocks, adjustment is accomplished by a small tray mounted on the rod where small weights are placed or removed to change the effective length, so the rate can be adjusted without stopping the clock.

The period of a pendulum increases slightly with the width (amplitude) of its swing. The rate of error increases with amplitude, so when limited to small swings of a few degrees the pendulum is nearly isochronous; its period is independent of changes in amplitude. Therefore, the swing of the pendulum in clocks is limited to 2° to 4°.