Optimization of Oscillation Damping in Systems with a Noninteger Number of Degrees of Freedom

Issues related to choosing 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-are discussed. Maximization of the degree of stability of the system is taken as an optimization criterion characterizing the efficiency of its oscillation damping. Two options for installing a damping device are discussed: either at the pendulum joint or parallel to the elastic element. In each case, the analytical solution of the optimization problem is found and is accompanied by a visual graphic illustration. In addition, a comparison of two cases of damping is carried out based on analysis of the maximum degree of stability and a conclusion about the viability of using both variants is made. The results obtained in this study are of interest from both theoretical and practical points of view, and the described plan for searching for the optimal solution can also be applied to solving other optimization problems in systems with a noninteger number of degrees of freedom.