146. Gas, in equilibrium at pressure po and mass density PO, is confined to a cylinder of length L and cross sectional area A. The right hand end of the cylinder is closed and fixed. At the left hand...

146. Gas, in equilibrium at pressure po and mass density PO, is confined to a cylinder of length L and cross sectional area A. The right hand end of the cylinder is closed and fixed. At the left hand end there is a frictionless and massless movable piston. In equilibrium the external force that must be exerted on the piston is of course fo = poA. However, suppose a small additional force is supplied by an external agency: the harmonic force f ( t ) = fo cos(wt). This produces small motions of the piston and thus small amplitude disturbances in the gas. Let c be the speed of sound in the gas; neglect viscosity. Let v ( t ) be the velocity of the piston. Compute v ( t ) .