Chapter 18, Problem 70P

A horizontal piston-cylinder system containing n mol of ideal gas is surrounded by air at temperature T₀ and pressure p₀. If the piston is displaced slightly from equilibrium, show that it executes simple harmonic motion with angular frequency ω = Ap₀/ $\sqrt{\text{MnR}{\text{T}}_0}$, where A and M are the piston area and mass, respectively. Assume the gas temperature remains constant.