In the current research, the aim is to provide the best mechanical damping design for damping the vibrations on a suspended object in a vibrating system that is subjected to base and shock excitations. The vibration model considered in two-dimensional form includes the degrees of freedom of vertical movement of the chamber and the hanging object inside it, their screws and the vertical movement of the center of the wheels. To simulate this two-dimensional model, two-connection and three-connection modes to the ceiling of the chamber are considered. Also, the base excitation frequency is taken into account by considering the average of the road surface profile with a wavelength of 1.2 meters and three speeds of 10, 15 and 20 meters per second to determine the high and low excitation frequency; Also, the application of shock force in a fraction of time in the form of Dirac's delta function is considered to check the performance of hangers under different stimulations. The extraction of the unknown longitudinal parameter of the placement of damping and springs relative to the center of mass of the suspended object, which perform the equivalent function of the hanger, as well as the value of the damping coefficient and their equivalent stiffness, has been used from programming in MATLAB software in the form of a multi-objective genetic algorithm optimization code. The results determine the best values of these parameters by considering the objective functions of the minimum ratio of force transfer to the suspended object inside the chamber compared to the base excitation and the maximum depreciation work done by the dampers in the vibrating system. The results show the superiority of the optimized model for three connections due to the reduction of the maximum amplitude and duration of vibration damping.