A cylindrical tube oriented vertically on Earth's surface, closed at the bottom and open at the top (height 100 m, cross sectional area 1 m2) initially contains air at a pressure of one atmosphere and temperature 300 K. A disc of mass m plugs the cylinder, but is free to slide up and down without friction. In equilibrium, the air in the cylinder is compressed to p = 2 atm while the air outside remains at 1 atm.
(a) What is the mass of the disc?
Next, the disc is displaced slightly in the vertical (z) direction and released.
(b) Assuming that the temperature remains fixed and that dissipation can be ig- nored, what is the frequency with which the disc oscillates?