Normal oscillations of a pendulum with a cavity filled with a viscoelastic fluid

In this paper, we consider the normal oscillations of a pendulum with a cavity completely filled with a viscoelastic fluid. The main spectral problem is formulated and the structure of its spectrum is studied. A connection is established between the solutions of the problem and the eigenvalue problem for a certain operator bundle. On this basis, information about the structure of the spectrum is supplemented, the questions of the basis of the root elements of the problem are studied.