Vibrations of linear multi-degree of freedom systems with and without damping. Systems with viscous, hysteretic and Coulomb damping. Influence coefficients, potential and kinetic energy expressions in matrix form. Eigenvalue problem and system response. Orthogonality of normal modes, expansion theorem. Unrestrained systems. Analytical methods, numerical methods and computational analysis of vibrations and mode shapes. Dunkerley’s formula, Rayleigh’s method, Holzer’s method, matrix iteration method, Jacobi’s method. Introduction to rotor dynamics.