Historical Setting

It is recorded that a chance observation of a swinging church lamp led Galileo to find that a pendulum made every swing in the same time, independent of the size of the arc. He used this discovery in measuring time in his astronomical studies. His experiments showed that the longer the pendulum, the longer is the time of its swing.

Christiaan Huygens determined the mathematical relationship between the length of the pendulum and the period of vibration when the arc of swing is small. He arrived at the formula:

where

• T is the period, or time for one complete swing,
• l is the length - the distance from the point of suspension to the center of gravity of the bob. Care has to be taken that the point of suspension is a point - this can be achieved by clamping the string frimly between two pieces of card.
• g is the acceleration of gravity.

In 1673, Huygens devised a practicable means of making a pendulum control the speed with which a clock mechanism runs. This led not only in the development of many types of clock, but also in the application of pendulum control to other mechanisms.

Problems and how they were overcome

Metal pendulums expand when heated (longer - therefore period increases!); to counteract the effect of temperature changes, compensation pendulums have been devised, many of them operating by the opposite expansion of different metals in compound rods.

Forces acting on the bob, such as air resistance and friction at the pivot point, affect its swing - great care is taken to minimise friction or movement at the pivot point and a pendulum in a vaccuum will not suffer air resistance (but most pendulum clocks do not need such a great expense!)