Vibrations and Waves [Hardcover]

This introductory text emphasises physical principles, rather than the mathematics. Each topic begins with a discussion of the physical characteristics of the motion or system. The mathematics is kept as clear as possible, and includes elegant mathematical descriptions where possible. Designed to provide a logical development of the subject, the book is divided into two sections, vibrations followed by waves. A particular feature is the inclusion of many examples, frequently drawn from everyday life, along with more cutting-edge ones. Each chapter includes problems ranging in difficulty from simple to challenging and includes hints for solving problems. Numerous worked examples included throughout the book.

Editors' Preface to the Manchester Physics Series xi

Author's Preface xiii

1 SIMPLE HARMONIC MOTION 1

1.1 Physical Characteristics of Simple Harmonic Oscillators 1

1.2 A Mass on a Spring 2

1.2.1 A mass on a horizontal spring 2

1.2.2 A mass on a vertical spring 5

1.2.3 Displacement, velocity and acceleration in simple harmonic motion 5

1.2.4 General solutions for simple harmonic motion and the phase angle φ 7

1.2.5 The energy of a simple harmonic oscillator 10

1.2.6 The physics of small vibrations 12

1.3 The Pendulum 17

1.3.1 The simple pendulum 17

1.3.2 The energy of a simple pendulum 19

1.3.3 The physical pendulum 22

1.3.4 Numerical solution of simple harmonic motion3 24

1.4 Oscillations in Electrical Circuits: Similarities in Physics 27

1.4.1 The LC circuit 27

1.4.2 Similarities in physics 29

PROBLEMS 1 29

2 THE DAMPED HARMONIC OSCILLATOR 33