A non-conducting piston of mass m and are ${\mathrm{S}}_0$ divides a non-conducting, closed cylinder as shown in the figure. A piston having mass $m$ is connected with the top wall of the cylinder by a spring of force constant $k$. The top part is evacuated and the bottom part contains an ideal gas at a pressure ${\mathrm{P}}_0$ in the equilibrium position. Adiabatic exponent $\mathrm{\gamma }$ and in equilibrium length of each part is $l$. (neglect friction). Find the angular frequency for small oscillation.