Vibrations Analysis presents concise but thorough fundamental statement of the theory, principles and methods. Topics covered include concepts and review of analytical dynamics, the basic single and the complex multiple degree of freedom systems using the Newton's law of motion, the energy method, matrix method, Lagrange's equations, influence coefficients, matrix iteration, the Holzer method, Jacobi's method and Chloleski decomposition method. An introduction to the theory of vibration of continuous systems is also included. The Rayleigh and Rayleigh-Ritz methods of determining the approximate natural frequencies are also discussed.