1. The problem statement, all variables and given/known data The closed cylinder of the figure has a tight-fitting but frictionless piston of mass M. the piston is in equilibrium when the left chamber has pressure p0 and length L0 while 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 on 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 << L0 find an expression for the oscillation period T. 2. Relevant equations for a. Not quite sure, All this chapter in the book really taught me was the Ideal Gas Law pV = nRT Given that the question is concerned that I include M I suppose they want me to use kinematics? I don't know how M (mass of the piston) affects the gasses, or ΔL. I know pressure = Force/Area, and Force = Mass X Acceleration -k X Δx since it's a spring for b. force of spring = -kΔx p1 = nRT/V1 V=A*L0 p1*v1 = p2*v2 for c. not sure 3. The attempt at a solution Note: spring is being compressed, p=0 on other side of piston first off, V1 = A*L0 then p1 = (-kΔL)/A (I'm lead to believe p = 0 when ΔL = 0 I need to fit in M somewhere to fulfill a. p1*A = Fsp = -kΔL or, since it's a Force, M*acceleration. need k, cross out F=Ma approach what does M effect? not volume not temperature movement pressure? Fsp? I wonder... Potential spring energy is Usp = 1/2k * Δx^2... Kinetic energy is 1/2m * v^2 could I turn the isothermal (p1v1 = p2v2) into kinematics? energy? forces to the right are sourced from p1 and forces to the left are sourced from the spring p1 = 1/V1 V1 = A*L0.... but plus ΔL if it ever gets larger or smaller p1 = 1/(A*(L0+ΔL)) equilibrium lets p1 also equal Fsp/A -k*ΔL/A = 1/(A*(L0+ΔL)) I think I am stuck here I need some clues, or hints as to how I should approach this. I feel that once I find out how M effects ΔL the rest wont be so hard!