Understanding Pendulums
Description
Despite their apparent simplicity, the behaviour of pendulums can be remarkably complicated. Historically, pendulums for specific purposes have been developed using a combination of simplified theory and trial and error. There do not appear to be any introductory books on pendulums, written at an intermediate level, and covering a wide range of topics. This book aims to fill the gap. It is written for readers with some background in elementary geometry, algebra, trigonometry and calculus. Historical information, where available and useful for the understanding of various types of pendulum and their applications, is included.
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. Interest in theoretical and practical aspects of pendulums, as applied to clocks, goes back more than four centuries. The concept of simple pendulums, which are idealised versions of real pendulums is introduced. The application of pendulums to clocks is described, with detailed discussion of the effect of inevitable differences between real pendulums and simple pendulums. In a clock, the objective is to ensure that the pendulum controls the timekeeping. However, pendulums are sometimes driven, and how this affects their behaviour is described. Pendulums are sometimes used for occult purposes. It is possible to explain some apparently occult results by using modern pendulum theory. For example, why a ring suspended inside a wine glass, by a thread from a finger, eventually strikes the glass. Pendulums have a wide range of uses in scientific instruments, engineering, and entertainment. Some examples are given as case studies.
Indexed in the Book Citation Index- Science (BKCI-S)
Reviews / Votes
From the reviews:
"The present volume is a more modest contribution and is essentially an introduction to the topic. . for a mathematically inclined audience, this is a nice book, introducing the more technological issues associated with the pendulum in an interesting way. The author uses elementary mathematics throughout, and accessible language. . this booklet is an original and worthwhile addition to the literature. . it is an ideal introduction to the fascinating world of the pendulum from the perspective of a professional engineer. I enjoyed reading it." (Giuseppe Saccomandi, Mathematical Reviews, August, 2013)
"Pook, a retired professional mechanical engineer and teacher, distinguishes it from others in the field by requiring that readers have a certain amount of mathematical knowledge to follow his discourse. In this, he largely succeeds. . But most of his discussion relates to very practical and useful applications in engineering. . The volume includes useful, clear diagrams and pictures to help the reader understand the material. Every chapter has extensive references, and there is a good index. Summing Up: Recommended. Lower-division undergraduates through professionals." (N. Sadanand, Choice, Vol. 49 (4), December, 2011)More details
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Content
Preface.- Notation.- 1 Introduction.- References.- 2 Simple Pendulums.- 2.1 Introduction.- 2.2 Simple Harmonic Motion.- 2.3 Analysis of a Simple Rod Pendulum.- 2.3.1 Acceleration due to Gravity.- 2.3.2 Accelerations of a Simple Rod Pendulum.- 2.3.3 Potential and Kinetic Energy of a Simple Rod Pendulum.- 2.3.4 Circular Error of a Simple Rod Pendulum.- 2.3.5 Effect of the Earth's Curvature.- 2.4 Analysis of a Simple String Pendulum.- 2.5 Spherical Rod Pendulum.- References.- 3 Variations on Simple Pendulums.- 3.1 Introduction.- 3.2 Compound Pendulum.- 3.3 Double Rod Pendulum.- 3.4 Blackburn Pendulum.- 3.5 Bifilar Pendulum.- 3.6 Rotating Simple Rod Pendulum.- 3.7 Quadrifilar Pendulum.- 3.7.1 Dual String Pendulum.- 3.8 Trapezium Pendulum.- 3.8.1 Dual Rod Pendulum.- 3.9 Double String Pendulum.- References.- 4 Pendulum Clocks.- 4.1 Introduction.- 4.2 Pendulum Quality Q.- 4.2.1 Damped Simple Harmonic Motion.- 4.2.2 Definition of Q.- 4.3 Buoyancy.- 4.4 Suspensions and Modes of Oscillation.- 4.4.1 Spring Suspensions.- 4.4.2 Pivot Suspensions.- 4.4.3 Knife Edge Suspensions.- 4.5 Effects of Escapements.- 4.6 Reduction of Effects of Circular Error.- References.- 5 Driven Pendulums.- 5.1 Introduction.- 5.2 Random Process Theory.- 5.2.1 Bandwidth.- 5.3 Driven Damped Simple Harmonic Motion.- 5.3.1 Periodic Driving.- 5.3.2 Random Driving.- 5.4 Horizontal Driving of Pendulums.- 5.4.1 Periodic Driving.- 5.4.2 Random Driving.- 5.5 Occult Uses of Pendulums.- References.- 6 Scientific Instruments.- 6.1 Introduction.- 6.2 Kater's Pendulum.- 6.3 Newton's Cradle.- 6.3.1 Modes of Oscillation.- 6.3.2 Theoretical Analysis.- 6.4 The Foucault Pendulum.- 6.4.1 Essential Features.- 6.4.2 Pumping.- 6.4.3 Motions of the Bob.- 6.5 Charpy Impact Testing Machine.- References.- 7 Engineering.- 7.1 Introduction.- 7.2 WattSteam Governor.- 7.3 Cable Car.- 7.4 Tension Leg Platform.- References.- 8 Entertainment.- 8.1 Introduction.- 8.2 Child's Swings.- 8.2.1 Pumping of Child's Swings.- 8.3 Child's Rocking Horse.- 8.4 Pendulum Harmonographs.- 8.5 Harmonograms and Pendulum Harmonographs.- 8.5.1 Lissajous Figures.- 8.5.2 Circular Harmony Curves.- 8.5.3 Miscellaneous Harmonograms.- 8.5.4 Some Practical Considerations.- References.- Index.