$1\mathrm{.}29$ Figure $1\mathrm{.}84$ shows an air spring. This type of spring is generally used for obtaining very low natural frequencies while maintaining zero deflection under static loads. Find the spring constant of this air spring by assuming that the pressure $p$ and volume $v$ change adiabatically when the mass $m$ moves.

FIGURE $1\mathrm{.}84$

Hint: $p$

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