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We study the motion of the coupled system, $\mathscr S$, constituted by aphysical pendulum, $\mathscr B$, with an interior cavity entirely filled with aviscous, compressible fluid, $\mathscr F$. The presence of the fluid maystrongly affect on the motion of $\mathscr B$. In fact, we prove that, underappropriate assumptions, the fluid acts as a damper, namely, $\mathscr S$ musteventually reach a rest-state. Such a state is characterized by a suitabletime-independent density distribution of $\mathscr F$ and a correspondingequilibrium position of the center of mass of $\mathscr S$. These results areproved in the very general class of weak solutions and do not require anyrestriction on the initial data, other than having a finite energy. Wecomplement our findings with some numerical tests. The latter show, among otherthings, the interesting property that ``large" compressibility favors thedamping effect, since it drastically reduces the time that $\mathscr S$ takesto go to rest.

On the Motion of a Pendulum with a Cavity Filled with a Compressible Fluid