Some spectral properties of an eigenvalue problem with spectral parameter contained in the boundary conditions

In this paper we consider a spectral problem with describes bending vibrations of a homogeneous rod, in cross-sections of which the longitudinal force acts, the left end of which is fixed, and the right end resiliently fastened and on this end an inertial mass is concentrated. We give the location of the eigenvalues on the real axis and the structure of root subspaces of this problem.