Understanding Pendulums pp 1-6 | Cite as

# Introduction

## Abstract

Perhaps the best known use of pendulums is as the basis of clocks in which a pendulum controls the rate at which the clock runs. Many clocks have visible pendulums. Indeed, the association of pendulums with clocks is so pervasive that, since the advent of quartz clocks, it is possible to buy clocks with visible swinging pendulums that are independent of the timekeeping of the clock. Interest in the behaviour of pendulums, in particular calculation of times of swing, dates back to the observation, usually attributed to Galileo, that the time of swing of a pendulum is independent of the amplitude of its oscillations. In other words the pendulum is isochronous. The story is that in 1581 Galileo was sitting in Pisa Cathedral, and compared the times of oscillations of suspended lamps with the pulse in his wrist. The seminal book on theoretical and practical aspects of pendulums, as applied to clocks, is ‘Horologium’ by Christiaan Huygens published in 1658. For the four centuries following Huygens’ seminal work pendulum behaviour was regarded as essentially regular. The important properties of a pendulum were assumed to be its time of swing, and the variability of the time of swing. Much effort was devoted to theoretical and practical aspects of improving the accuracy of pendulums used to control clocks. Scientific applications of pendulums include the Foucault pendulum used to demonstrate rotation of the Earth, and the Charpy impact test, used to measure the fracture resistance of metals. Industrial applications include the Watt steam governor used to regulate steam engines and the tension leg platforms used for the offshore recovery of oil and gas. Recreational uses include children’s swings, and pendulum harmonographs used to draw figures known as harmonograms. Pendulums are sometimes used for occult purposes. More recently it has been appreciated that pendulum behaviour can be irregular. In other words a pendulum can be a chaotic system. This means that chaos theory is needed for understanding of pendulum behaviour. In scientific terminology chaos is shorthand for chaotic dynamics and therefore has a different meaning from its everyday meaning of utter confusion. Chaotic dynamics is used to describe the chaotic behaviour of a chaotic system. Chaotic behaviour is not random. If the initial conditions are known with sufficient accuracy then the subsequent behaviour can, in principle, be predicted precisely. In practice, in a chaotic system the subsequent behaviour is so sensitive to the initial conditions that an attempt to reproduce the initial conditions is never sufficiently precise, and the outcome on successive attempts can vary widely.

## Keywords

Chaotic System Chaotic Dynamic Chaotic Behaviour Practical Aspect Fracture Resistance## References

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