Model problem on normal oscillations of partially dissipative hydrosystem

In this paper, we consider a model spectral problem that preserves all the features of the real problem of normal oscillations of the hydrodynamic
a system consisting of two incompressible homogeneous liquids placed in an arbitrary vessel. In this case, a liquid of higher density is viscous,
and the smaller one is ideal. The study of the spectrum of the problem was carried out on the basis of the study of the transcendental characteristic equation with respect to
complex damping decrement of normal oscillations.