Restoration of two coefficients in the model of string oscillations with an elastically fixed end

We consider the inverse problem of simultaneous determination of two coefficients in the model of small transverse oscillations of a homogeneous bounded string, on whose one end an elastic force acts, and whose other end is not fixed. The oscillation process is modeled by a non-homogeneous equation of hyperbolic type, with the non-homogeneity in the equation represented by multipliers depending on different arguments. The specified values of the solution of the direct problem at the free end of the string constitute some additional information for solving the inverse problem. In this context, within the framework of posing the inverse problem, it is required to define the function in the boundary condition of the third kind as well as the functional multiplier in the non-homogeneity of the equation. The paper establishes conditions for solvability of the inverse problem, some properties of its solution, and proposes an algorithm for numerical approximation of the solution