Optimization of oscillation damping in systems with a non-integer number of degrees of freedom

The paper discusses issues related to the choice of the optimal damping for a system with one and a half degrees of freedom - a pendulum with an elastic-movable suspension point in the presence of viscous friction. Maximization of the degree of stability of the system is taken as an optimization criterion characterizing the efficiency of damping oscillations. Two options for installing a damping device are discussed - either in the pendulum joint, or parallel to the elastic element. The analytical solution of the optimization problem is performed in each case, and it is accompanied by a visual graphic illustration. In addition, a comparison of two cases of damping is given on the basis of analysis of the maximum degree of stability and a conclusion about the advisability of using one or another option is made. The obtained results are of interest both in theoretical and practical terms, and the described plan for finding the optimal solution can also be applied to solving other optimization problems in systems with a non-integer number of degrees of freedom.