Forced Vibration with non harmonic and transient excitation of single degree freedom systems: Fourier analysis, Response to arbitrary loading (Duhamel’s Integral), Impulse response, Mechanical shock, Parametric Excitation. Two degree Freedom System, Multi-degree Freedom systems, modal analysis, Matrix iteration Method, Transfer matrix Method, Myklestadt-Prohl Method, Rayleigh’s minimum principle, Stodola’s Method, Hoizer’s Method. Vibrations of Continuous systems governed by wave equation and Euler Bernoulli equation, strings, membranes, rods, beams. Experimental Methods in Vibration Analysis, industrial applications - rotors and other systems, vibration standards. Vibration Monitoring and analysis: Introduction, Machinery signatures, Selection of Transducers. Analysis Techniques, Machine failure modes, Measurement location, Vibration severity criteria, Vibration frequency analysis. Permanent Monitoring, Case studies.