This fully revised and updated third edition covers the physical and mathematical fundamentals of vibration analysis, including single degree of freedom, multi-degree of freedom, and continuous systems. Adding a new chapter on special topics such as motion control, impact dynamics, and nonlinear dynamics, this textbook imparts a sound understanding of the fundamental theory of vibration and its applications. In a simple and systematic manner, it presents techniques that can easily be applied to the analysis of vibration of mechanical and structural systems. Unlike other texts on vibrations, the approach is general, based on the conservation of energy and Lagrangian dynamics, and develops specific techniques from these foundations in clearly understandable stages. Suitable for a one-semester course on vibrations, the book presents new concepts in simple terms and explains procedures for solving problems in considerable detail. It contains numerous exercises, examples and end-of-chapter problems. Features updates and revisions to all chapters as well as new sections on motion control, impact dynamics, and nonlinear dynamics; Provides lucid yet rigorous review of the mathematics needed for the solution of the vibration equations; Presents complete coverage of the theory of vibration with focus of the fundamentals, numerical and computer methods;; Reinforces concepts with numerous exercises and examples and end-of-chapter problems; Includes a Fortran code for solving ODEs of nonlinear vibration systems.