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Sorry - I was trying to follow the thread - someone had proposed letting a weight fall through mgh to a stop. If there is no stop then the mass certainly oscillates. However, again following the thread of adiabatic, the oscillation follows the same P-V adiabatic curve during the oscillation as it does in the slow adiabat (neglecting for the moment the sound wave, etc., points that have been raised on this thread).
It overshoots the final stopping point (h) along that adiabat and then retraces itself - the net result being the area under the reversible quasi-equilibrium process - mgh.