A technology for evaluating the dynamic properties of mechanical vibration systems within the framework of structural and mathematical modeling methods with the use of dynamic characteristics of the structure of vibration fields of technological machines has been developed. We consider the problem of developing a mathematical model that allows us to correct the dynamic state depending on the system parameters based on local estimates of the properties of the vibration field. The ratio of reactions is used to evaluate the dynamic state of the vibration field. The coupling coefficient of external harmonic perturbations and the mass-inertia characteristic of a device for converting motion are considered as parameters of a mechanical oscillatory system. Based on a model with two degrees of freedom and two external influences, a detailed method for constructing mathematical models for evaluating local features of the vibration fields of technological machines is proposed. The obtained analytical expressions allow us to construct diagrams of the characteristics of mechanical oscillating systems depending on the parameters of the adjustment tools.