"Mechanical Vibrations" designed as a text for senior undergraduate and graduate students covers both analytical and physical aspects of mechanical vibrations. Each chapter consists of a concise but thorough fundamental statement of the theory, principles and methods. The classical methods of mechanical vibrations i.e. free vibration of single degree of freedom systems, harmonically forced vibrations of single degree of freedom systems, general forcing conditions and response, two degree of freedom systems, multi degree of freedom systems, analytical dynamics Lagrange's equation of motion, vibration of continuous systems, and approximate methods for finding natural frequencies and mode shapes, dynamic response by direct numerical integration methods, vibration control, and introduction to finite element method are covered in detail. In addition to students, practicing engineers should find this book immensely useful. All the end-of chapter problems are fully solved in the "Solution Manual" available only to Instructors.