S is a piston of mass M which can slide inside a cylinder without friction. The walls of the cylinder is adiabatic and the piston is diathermic and area of cross section of cylinder is A. Length of the cylinder is 2l_0. Initial pressure of each chamber is P_0. Volume of the chambers are equal. Initially spring is unstretched and has spring constant k. The spring is fixed with piston and wall of the cylinder as shown in the figure. Find out its time period when piston is given small displacement.

S is a piston of mass M which can slide inside a cylinder without fric

1.	S is a piston of mass M which can slide inside a cylinder without friction. The walls of the cylinder is adiabatic and the piston is diathermic and area of cross section of cylinder is A. Length of the cylinder is 2l_0. Initial pressure of each chamber is P_0. Volume of the chambers are equal. Initially spring is unstretched and has spring constant k. The spring is fixed with piston and wall of the cylinder as shown in the figure. Find out its time period when piston is given small displacement.
Answer» SOLUTION :`T=2pisqrt((MI_0)/(2P_0 A+Kl_0))`