Except for digressions in Chapters 8 and 17, this book is a highly unified treatment of simple oscillations and waves. The phenomena treated are "simple" in that they are de scribable by linear equations, almost all occur in one dimension, and the dependent variables are scalars instead of vectors or something else (such as electromagnetic waves) with geometric complications. The book omits such complicated cases in order to deal thoroughly with properties shared by all linear os cillations and waves. The first seven chapters are a sequential treatment of electrical and mechanical oscillating systems, starting with the simplest and proceeding to systems of coupled oscillators subjected to ar bitrary driving forces. Then, after a brief discussion of nonlinear oscillations in Chapter 8, the concept of normal modes of motion is introduced and used to show the relationship between os cillations and waves. After Chapter 12, properties of waves are explored by whatever mathematical techniques are applicable. The book ends with a short discussion of three-dimensional vii viii Preface problems (in Chapter 16), and a study of a few aspects of non linear waves (in Chapter 17).
Author(s): Ingram Bloch (auth.)
Edition: 1
Publisher: Springer US
Year: 1997
Language: English
Pages: 318
Tags: Physical Chemistry
Front Matter....Pages i-x
Undamped and Undriven Oscillators and LC Circuits....Pages 1-20
The Effect of Damping....Pages 21-32
Sinusoidally Driven Oscillators and Circuit Loops....Pages 33-50
Sums of Sinusoidal Forces or EMF’s—Fourier Analysis....Pages 51-72
Integration in the Complex Plane....Pages 73-87
Evaluation of Certain Fourier Integrals—Causality, Green’s Functions....Pages 88-103
Electrical Networks....Pages 104-119
Nonlinear Oscillations....Pages 120-150
Coupled Oscillators without Damping—Lagrange’s Equations....Pages 151-160
Matrices—Rotations—Eigenvalues and Eigenvectors—Normal Coordinates....Pages 161-180
Some Examples of Normal Coordinates....Pages 181-196
Finite One-Dimensional Periodic Systems, Difference Equations....Pages 197-215
Infinite One-Dimensional Periodic Systems—Characteristic Impedance....Pages 216-229
Continuous Systems, Wave Equation, Lagrangian Density, Hamilton’s Principle....Pages 230-250
Continuous Systems, Applied Forces, Interacting Systems....Pages 251-266
Other Linear Problems....Pages 267-289
Nonlinear Waves....Pages 290-308
Back Matter....Pages 309-317
