The Pendulum A Case Study in Physics

by Baker, Gregory L.; Blackburn, James A.

• ISBN13: 9780199557684
• ISBN10: 0199557683
• Format: Paperback
• Copyright: 2009-01-27
• Publisher: Oxford University Press

Summary

The pendulum: a case study in physics is a unique book in several ways. Firstly, it is a comprehensive quantitative study of one physical system, the pendulum, from the viewpoint of elementary and more advanced classical physics, modern chaotic dynamics, and quantum mechanics. In addition, coupled pendulums and pendulum analogs of superconducting devices are also discussed. Secondly, this book treats the physics of the pendulum within a historical and cultural context, showing, for example, that the pendulum has been intimately connected with studies of the earth's density, the earth's motion, and timekeeping. While primarily a physics book, the work provides significant added interest through the use of relevant cultural and historical vignettes. This approach offers an alternative to the usual modern physics courses. The text is amply illustrated and augmented by exercises at the end of each chapter.

Author Biography

Gregory L. Baker is Professor of Physics at Bryn Athyn College of the New Church, Pennsylvania, USA. James A. Blackburn is Professor of Physics at Wilfrid Laurier University, Ontario, Canada.

Table of Contents

Introduction	p. 1
Pendulums somewhat simple	p. 8
The beginning	p. 8
The simple pendulum	p. 9
Some analogs of the linearized pendulum	p. 13
The spring	p. 13
Resonant electrical circuit	p. 15
The pendulum and the earth	p. 16
The military pendulum	p. 19
Compound pendulum	p. 20
Kater's pendulum	p. 21
Some connections	p. 23
Exercises	p. 24
Pendulums less simple	p. 27
O Botafumeiro	p. 27
The linearized pendulum with complications	p. 29
Energy loss-friction	p. 29
Energy gain-forcing	p. 34
Parametric forcing	p. 42
The nonlinearized pendulum	p. 45
Amplitude dependent period	p. 45
Phase space revisited	p. 51
An electronic "Pendulum"	p. 53
Parametric forcing revisited	p. 56
A pendulum of horror	p. 63
Exercises	p. 64
The Foucault pendulum	p. 67
What is a Foucault pendulum?	p. 67
Frames of reference	p. 71
Public physics	p. 74
A quantitative approach	p. 75
Starting the pendulum	p. 78
A darker side	p. 85
Toward a better Foucault pendulum	p. 86
A final note	p. 89
Exercises	p. 91
The torsion pendulum	p. 93
Elasticity of the fiber	p. 93
Statics and dynamics	p. 95
Free oscillations without external forces	p. 96
Free oscillations with external forces	p. 98
Damping	p. 98
Two historical achievements	p. 99
Coulomb and the electrostatic force	p. 99
Cavendish and the gravitational force	p. 104
Scaling the apparatus	p. 108
Modern applications	p. 108
Ballistic galvanometer	p. 108
Universal gravitational constant	p. 110
Universality of free fall: Equivalence of gravitational and inertial mass	p. 113
Viscosity measurements and granular media	p. 117
Exercises	p. 119
The chaotic pendulum	p. 121
Introduction and history	p. 121
The dimensionless equation of motion	p. 125
Geometric representations	p. 126
Time series, phase portraits, and Poincare sections	p. 127
Spectral analysis	p. 130
Bifurcation diagrams	p. 133
Characterization of chaos	p. 135
Fractals	p. 135
Lyapunov exponents	p. 138
Dynamics, Lyapunov exponents, and fractal dimension	p. 142
Information and prediction	p. 144
Inverting chaos	p. 147
Exercises	p. 150
Coupled pendulums	p. 153
Introduction	p. 153
Chaotic coupled pendulums	p. 161
Two-state model (all or nothing)	p. 164
Other models	p. 168
Applications	p. 170
Synchronization machine	p. 170
Secure communication	p. 173
Control of the chaotic pendulum	p. 176
A final weirdness	p. 183
Exercises	p. 185
The quantum pendulum	p. 189
A little knowledge might be better than none	p. 189
The linearized quantum pendulum	p. 192
Where is the pendulum?-uncertainty	p. 196
The nonlinear quantum pendulum	p. 200
Mathieu equation	p. 201
Microscopic pendulums	p. 203
Ethane-almost free	p. 204
Potassium hexachloroplatinate-almost never free	p. 206
The macroscopic quantum pendulum and phase space	p. 208
Exercises	p. 209
Superconductivity and the pendulum	p. 211
Superconductivity	p. 211
The flux quantum	p. 214
Tunneling	p. 215
The Josephson effect	p. 216
Josephson junctions and pendulums	p. 220
Single junction: RSJC model	p. 220
Single junction in a superconducting loop	p. 224
Two junctions in a superconducting loop	p. 226
Coupled josephson junctions	p. 228
Remarks	p. 230
Exercises	p. 230
The pendulum clock	p. 233
Clocks before the pendulum	p. 233
Development of the pendulum clock	p. 235
Galileo (1564-1642)	p. 235
Huygens (1629-1695)	p. 235
The seconds pendulum and the meter: An historical note	p. 244
Escapements	p. 246
Temperature compensation	p. 249
The most accurate pendulum clock ever made	p. 252
Reflections	p. 255
Exercises	p. 255
Pendulum Q	p. 258
Free pendulum	p. 258
Resonance	p. 259
Some numbers from the real world	p. 261
The inverted pendulum	p. 263
The double pendulum	p. 267
The cradle pendulum	p. 270
The Longnow clock	p. 273
The Blackburn pendulum	p. 275
Bibliography	p. 276
Index	p. 286
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