  We study the motion of the coupled system, $\mathscr S$, constituted by a
physical pendulum, $\mathscr B$, with an interior cavity entirely filled with a
viscous, compressible fluid, $\mathscr F$. The presence of the fluid may
strongly affect on the motion of $\mathscr B$. In fact, we prove that, under
appropriate assumptions, the fluid acts as a damper, namely, $\mathscr S$ must
eventually reach a rest-state. Such a state is characterized by a suitable
time-independent density distribution of $\mathscr F$ and a corresponding
equilibrium position of the center of mass of $\mathscr S$. These results are
proved in the very general class of weak solutions and do not require any
restriction on the initial data, other than having a finite energy. We
complement our findings with some numerical tests. The latter show, among other
things, the interesting property that ``large" compressibility favors the
damping effect, since it drastically reduces the time that $\mathscr S$ takes
to go to rest.
