In this paper an effort has been made to model and damp a rotating flexible beam with a rotary joint. In this work bending of flexible beam is considered using Euler-Bernoulli beam theory. To model a flexible beam, which is essentially a continuous system, it is discretized by using finite element method. After finding the expression for displacement at any point using finite element method, the dynamic equations of motion are derived using Lagrangian formulation. Time response results are obtained for undamped and viscous damped systems. Finally flexible beam is modelled as -a typical laminated composite beam made up of number of layers of passive damping coating and a magnetostrictive material. A combined passive and active damping strategy in hybrid mode using combination of layers of ferromagnetic (passive) and smart (active) magnetostrictive (Terfenol-D) materials is proposed.