Oscillations of a Piston A vertical cylinder of radius r contains a quantity of ideal gas and is fitted with a piston with mass m that is free to move (Fig. 19.34). The piston and the walls of the cylinder are frictionless and the entire cylinder is placed in a constant-temperature bath. The outside air pressure is p0. In equilibrium, the piston sits at a height h above the bottom of the cylinder.
(a) Find the absolute pressure of the gas trapped below the piston when in equilibrium.
(b) The piston is pulled up by a small distance and released. Find the net force acting on the piston when its base is a distance h + y above the bottom of the cylinder, where y is much less than h.
(c) After the piston is displaced from equilibrium and released, it oscillates up and down. Find the frequency of these small oscillations. If the displacement is not small, is the oscillations simple harmonic? How can you tell?

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Open to outside air, pressure Po -Piston, mass m Idcal- gas