Determination of boundary conditions for the fastening of strings from vibration eigenfrequencies in a medium with a variable symmetric elasticity coefficient

This paper considers the inverse problem of identifying boundary conditions for the problem of vibrations of a string in an elastic external medium, whose elasticity coefficient is described by an asymmetric potential. It is shown that, in contrast to the case of a symmetric potential, the boundary conditions can be uniquely identified, but this requires the use of three, rather than two, vibration eigenfrequencies. Cases are considered in which unique identification using two eigenfrequencies is possible. Methods for determining boundary conditions from two and three eigenfrequencies are proposed. The error of the methods is analyzed.