Abstract
In the current paper, the problem of bending vibrations of a beam in which the binding on the right end is unknown and not available for visual inspection is studied. The main objective is to study an inverse problem: find additional unknown boundary conditions by additional spectral data, i.e., the conditions of fixing the right end of the rod. In this work, unlike many other works, as such additional conditions we choose the first natural frequencies (eigenvalues) of two new problems corresponding to the problem of bending vibrations of a beam with loads of different weights at the central point.