The article considers the spatial vibrations of the system consisting of a cable and a solid body of arbitrary spatial configuration. The problem is solved in a geometrically linear formulation, but with a full account of the stiffness and inertial characteristics. Energy dissipation is taken into account, which has expressed hysteresis type. Physical relations, considering the energy dissipation, are formulated on the basis of kinematic equation, the parameters of which are identified using experimental data on the hysteresis curves of the limit cycle.