= Adiabatic gas-spring piston period
{title2=$\tau=2\pi\sqrt{mV_0/(\gamma p_0A^2)}$}
A frictionless piston of area $A$ and mass $m$ supported by gas has $p_0=p_{\rm ext}+mg/A$. Small displacement $x$ changes its <volume (thermodynamics)> by $Ax$. The local <isentropic compressibility> gives $\delta p=-\gamma p_0Ax/V_0$, so <Newton's second law> becomes $m\ddot x=-\gamma p_0A^2x/V_0$. The period follows. Gas inertia and heat leakage are neglected, and internal equilibration must be faster than the oscillation.
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