The Physics of Oscillations and Waves: With Applications in Electricity and Mechanics [Hardcover]

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).1 Undamped and Undriven Oscillators and LC Circuits.- 2 The Effect of Damping.- 3 Sinusoidally Driven Oscillators and Circuit Loops.- 4 Sums of Sinusoidal Forces or EMFsFourier Analysis.- 5 Integration in the Complex Plane.- 6 Evaluation of Certain Fourier IntegralsCausality, Greens Functions.- 7 Electrical Networks.- 8 Nonlinear Oscillations.- 9 Coupled Oscillators without DampingLagranges Equations.- 10 MatricesRotationsEigenvalues and EigenvectorsNormal Coordinates.- 11 Some Examples of Normal Coordinates.- 12 Finite One-Dimensional Periodic Systems, Difference Equations.- 13 Infinite One-Dimensional Periodic SystemsCharacteristic Impedance.- 14 Continuous Systems, Wave Equation, Lagrangian Density, Hamiltons Principle.- 15 Continuous Systems, Applied Forces, Interacting Systems.- 16 Ol/