The closed cylinder of FIGURE CP18.74 has a tight-fitting but frictionless piston of mass M. The piston is in equilibrium when the left chamber has pressure p₀and length L₀while the spring on the right is compressed by ΔL.
a. What is ΔL in terms of p₀, L₀, A, M, and k?
b. Suppose the piston is moved a small distance x to the right.
Find an expression for the net force (F_x)_neton the piston. Assume all motions are slow enough for the gas to remain at the same temperature as its surroundings.
c. If released, the piston will oscillate around the equilibrium position. Assuming x << L₀find an expression for the oscillation period T.

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Mass M Area A p =0 Po Lo Compressed AL FIGURE CP18.74