Opuscula Math. 35, no. 2 (2015), 143-159
On small vibrations of a damped Stieltjes string
Abstract. Inverse problem of recovering masses, coefficients of damping and lengths of the intervals between the masses using two spectra of boundary value problems and the total length of the Stieltjes string (an elastic thread bearing point masses) is considered. For the case of point-wise damping at the first counting from the right end mass the problem of recovering the masses, the damping coefficient and the lengths of the subintervals by one spectrum and the total length of the string is solved.
Keywords: damping, Dirichlet boundary condition, point mass, Hermite-Biehler polynomial, continued fraction, eigenvalues.
Mathematics Subject Classification: 35Q99, 39A99.