Vibration is occasionally "desirable". But, more often, vibration is undesirable, wasting energy and creating unwanted sound-noise. So, to use the desirable vibrations & to remove or to reduce undesirable vibrations, we need to study the vibrations. The aim of the project (in this book) is to investigate the use of a Vibration Absorber with viscoelastic damping to optimally control the vibration of a beam. A main beam, with fixed-fixed boundary condition is selected after an exhaustive literature study. The project tasks have been decomposed into optimum design & analysis and fabrication of vibration absorber with viscoelastic damping. The equations of motion of the system have been derived to find the vibration response with and without absorber for optimization. The Classical and Den Hartog optimization methods are used to optimize the parameter and optimum values are found out. The experiments are performed on main beam with absorbers having viscoelastic damping (unconstrained and constrained treatments), and the experimental values are compared with the theoretical values.