The Physics of Oscillations and Waves: With Applications in Electricity and Mechanics / Edition 1

by Ingram Bloch

Overview

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).

Product Details

ISBN-13:	9780306457210
Publisher:	Springer US
Publication date:	06/30/1997
Series:	Technology
Edition description:	1997
Pages:	318
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

Undamped and Undriven Oscillators and LC Circuits. The Effect of Damping. Sinusoidally Driven Oscillators and Circuit Loops. Sums of Sinusoidal Forces or EMF's - Fourier Analysis. Integration in the Complex Plane. Evaluation of Certain Fourier Integrals - Causality, Green's Functions. Electrical Networks. Nonlinear Oscillations. Coupled Oscillators without Damping - Lagrange's Equations. Matrices - Rotations - Eigenvalues and Eigenvectors - Normal Coordinates. Some Examples of Normal Coordinates. Finite One-Dimensional Periodic Systems. Difference Equations. Infinite One-Dimensional Periodic Systems - Characteristic Impedance. Continuous Systems. Wave Equation. Lagrangian Density. Hamilton's Principle. Continuous Systems. Applied Forces. Interacting Systems. Other Linear Problems. Nonlinear Waves. Answers to Selected Problems. Index.

Editorial Reviews

An accessible introduction to mathematics of linear oscillations and waves, designed to prepare advanced undergraduate and graduate physics majors for the study of quantum mechanics. The first seven chapters offer a sequential treatment of electrical and mechanical oscillating systems, explaining mathematical techniques in the context of actual physical problems. Later chapters treat normal modes of motion, properties of waves, and three-dimensional problems, plus nontraditional subjects such as ladder networks and characteristic impedance. Includes chapter exercises and selected answers. Assumes some knowledge of linear differential equations and complex numbers. Annotation c. by Book News, Inc., Portland, Or.

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