Mechanical and Electromagnetic Vibrations and Waves

Table of Contents

Preface

Chapter 1. Free Oscillations

1.1. Oscillations and waves, period and frequency

1.2. Simple harmonic vibrations: differential equation and linearity

1.3. Complex representation and phasor representation

1.4. Point mass subject to a force–Kx

1.5. Angular oscillations

1.6. Damped oscillations

1.7. Dissipation of the energy of a damped oscillator

1.8. Oscillating LCR circuits

1.9. Small oscillations of a system with one degree of freedom

1.10. Nonlinear oscillators

1.11. Systems with two degrees of freedom

1.12. Generalization to systems with n degrees of freedom

1.13. Normal variables for systems with n degrees of freedom*

1.14. Summary

1.15. Problem solving suggestions

1.16. Conceptual questions

1.17. Problems

Chapter 2. Superposition of Harmonic Oscillations, Fourier Analysis

2.1. Superposition of two scalar and isochronous simple harmonic oscillations

2.2. Superposition of two perpendicular and isochronous vector oscillations, polarization

2.3. Superposition of two perpendicular and non-isochronous oscillations

2.4. Superposition of scalar non-synchronous harmonic oscillations, beats

2.5. Fourier analysis of a periodic function

2.6. Fourier analysis of a non-periodic function

2.7. Fourier analysis of a signal, uncertainty relation

2.8. Dirac delta-function

2.9. Summary

2.10. Problem solving suggestions

2.11. Conceptual questions

2.12. Problems

Chapter 3. Forced Oscillations

3.1. Transient regime and steady regime

3.2. Case of a simple harmonic excitation ...