# Mechanical Vibration

*Mechanical vibration is defined as the measurement of a periodic process of oscillations with respect to an equilibrium point. This book should provide essential concepts involving vibrational analysis, uncertainty modeling, and vibration control. It should also give a good fundamental basis in computational results, mathematical modeling and assessment in performance of different systems and system components. Attention will be paid to vibrating systems such as beams, strings, plates and membranes, vibration isolation, critical speeds, the balancing of rotating and reciprocating machinery. Basic principles of control theory will be presented from feedback control systems. Finally, chapters will include numerous example problems and possibly projects.*

## Contents

### Introduction & Background

- Distinguishing Mechanical Vibration
- Prerequisites
- Background & Models
- Idealization & Formulation
- Equilibrium
- Second Law of Motion
- Units

### Single Degree of Freedom: Introduction

- Deterministic Modeling
- Damping, Mass & Stiffness
- Electrical Analogy and relations
- Equations of Motion
- Formulation of Energy
- Lagrange Form Applied
- Pendulum Motion
- Free Vibration without Damping
- Harmonic forced without damping
- Vibrational Resonance
- Practice Problems

### Single Degree of Freedom: Damping

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