Shaft misalignment, rotor unbalance, rubbing, bearing faults and crack are the commonly observed faults in the Rotor-dynamic systems. Vibration signature is one of the best way for analysis of rotor bearing faults. In the present study, simply supported flexible shaft with a rigid disc carried by the flexible bearings at both the ends has been considered for the observations. Effect of gyroscopic moment, rotatory inertia and shear effect has been taken into account with the finite element approach. The bearing is considered as linear stiffness and damping and also do the comparison between Euler-Bernoulli and Timoshenko beam theory. The forward and backward whirl speed of rotor bearing system for different modes at various system parameters has been analysed with the help of Campbell diagram, Time responses and Fourier spectrum. Modes shapes of transverse displacements are shown for different modes of the system. The system equation is developed with the help of Lagrange’s equation, Hamilton principle and Galerkin method, the system finite differential equation has been analysed using the Newmark Integral method. Both free and forced vibration considering rotor unbalance and shaft misalignment have been analysed with the help of Fast Fourier Transformations (FFT) and Time responses, phase portrait and Poincare by the Finite element and experimentally. The base excitation analysis is done numerically.