A generalized model of the damper is proposed in the form of the equivalent Voigt model for viscoelastic materials, which fully correlates with the differential equation for induced oscillations in the system with a damper. The relations of parameters of the differential equation and parameters of the equivalent Voigt model with parameters of various models for viscoelastic materials and with components of the complex elastic modulus of these models are established. An approach for the assessment of the damper influence on the oscillation level of various elements in the analyzed system that occur under the impact of a coercive force of different frequencies is proposed for the mechanical system. It is presented in the form of the model with lumped parameters. Parameters of viscoelastic materials, which are suitable for use in dampers in the designed mechanical system, are determined based on obtained estimations. Thus, the proposed approach to the analysis of the behaviour of viscoelastic dampers allows us to determine the requirements for viscoelastic materials suitable for use in the designed systems. Also, it allows us to determine frequency response characteristics of dampers with known frequency dependences of storage modulus and loss modulus of the used viscoelastic materials.