Aerospace Instrument-Making Annotation << Back Method of Preсise Determination of Oscillation Parameters in Control Systems of One Class Using Asymptotic Estimates Shumilov Yu.Yu., Zhukov I.Yu. The article proposes a method for the exact solution of differential equations of linear models of dynamic systems with constant parameters or with a variable gain in the feedback. This problem is relevant in cases where the accuracy of the solution is of fundamental importance for determining the correct settings of the system, otherwise the consequences of even minor errors in determining the parameters, for example, the bifurcation point, when using the numerical method can lead to serious consequences, such as the failure of the system. A limitation for the application of the proposed method is the order of the differential equation of the system, which ensures the possibility of solving the characteristic equation in radicals. An example of such systems is the automatic control system for a heavy aircraft. Since in this case radio engineering means are used to determine the deviation of the aircraft from the glide path, the feedback contains a non-constant coeffi cient, due to which this system belongs to the class of systems with a singular point, the numerical solution of whose equations requires complex verifi cation and control during the modeling process. In this article, the main class of systems is considered to be a servo system, for which it is necessary to know with high accuracy the permissible frequency intervals of the input signal in order to exclude the possibility of linear resonance. An example of a fourth-order system is considered, for which, thanks to the use of the root hodograph method, it was possible to establish the possibility of resonance, thereby simplifying the problem and then obtaining the exact value of the resonance frequency even without using the Cardano or Ferrari formulas. Keywords: linear system, transfer function, Cardano’s formulas, root godograph. DOI: 10.25791/aviakosmos.8.2026.1578 Pp. 50-55.