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The Pendulum: A Case Study in Physics

Gregory L. Baker and James A. Blackburn
Oxford University Press
Publication Date: 
Number of Pages: 
[Reviewed by
William J. Satzer
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It’s an entire book about the pendulum, and quite a good one at that. The Pendulum: A Case Study in Physics is an unusual book from several perspectives. It takes a radically thematic approach to the teaching of physics. Organized around a single physical system, it uses the pendulum as a model for the interplay of classical, chaotic and quantum dynamics. This book also explores historical and cultural interrelationships among the various disciplines of physics and technology. In addition, the authors introduce us to a remarkable variety of historical figures involved in one way or another with the pendulum.

Having prepared the reader for an unorthodox presentation in their introduction, the authors proceed from the simplest pendulum system to progressively more complex ones. It is a very natural approach akin to a musical study with theme and variations. The simple pendulum with a small amplitude of oscillation, the very paradigm of simple harmonic motion, is introduced as a linear system. In this setting the authors describe the concepts of period, frequency, resonance and the conservation of energy as well as phase space and Fourier spectra, basic tools for the analysis of dynamics.

The first variations we see are damped and driven pendulum systems — still linear. Nonlinear systems are introduced — again via the pendulum — by removing the small amplitude assumption. There are several fresh examples and applications throughout this book. One of them is O Botafumiero, a giant censer (an incense burner) in the cathedral of Santiago de Compostela in northern Spain. O Botafumiero is a parametric pendulum whose length is periodically shortened by a pumping action carried out by a squad of men and a huge support mechanism. Dynamically O Botafumiero behaves much like a self-pumped swing.

A good deal of the charm of this book derives from examples like this one. The authors are loath to rely on the usual stock of golden oldies. After the introductory chapters, the authors take up the Foucault pendulum (doing a very nice job on the physics and the historical background) and the torsion pendulum. Next we meet the chaotic pendulum, and though that the characterization of chaos and the tools used to describe it. Here we get a fairly standard treatment, but it is clear, careful and well-integrated with the themes of the book.

Coupled pendulums — a source of wonderful applications (including, for example, secure communications) are treated next. The quantum pendulum follows, with a separate chapter on application to Josephson junctions and superconductivity. The last chapter takes up the pendulum clock.

Prerequisites for this material are first-year calculus, some exposure to ordinary differential equations, and bit of introductory physics. There are a modest number of exercises at the end of each chapter. These tend to be non-routine; a companion website provides a solution manual. The text is laid out well with wide margins and very good use of photographs, figures and charts.

This book could be the basis of an excellent course in applied mathematics. The instructor could pick and choose topics of interest, and have at hand a coherent theme and a marvelous collection of examples and applications.

Bill Satzer ( is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.


1. Introduction 
2. Pendulums somewhat simple 
3. Pendulums less simple 
4. The Foucault pendulum 
5. The torsion pendulum 
6. The chaotic pendulum 
7. Coupled pendulums 
8. The quantum pendulum 
9. Superconductivity and the pendulum 
10. The pendulum clock 
A. Pendulum Q 
B. The inverted pendulum 
C. The double pendulum 
D. The cradle pendulum 
E. The long now clock 
F. The Blackburn pendulum