Mathematical study of the small oscillations of a pendulum containing a viscous liquid

The authors study the small oscillations of a pendulum containing a viscous liquid.Using the principle of virtual work, they determine the equations of motions and the variational formulation of the problem. Renouncing a little long method of the Russian scientists, they obtain directly from the variational equation, an operator equation in a Hilbert space.The corresponding bundle of operators belongs to a known class, as that the authors can study the spectrum of the problem and specify the set of eigenvalues according to the coefficient of viscosity.