A gas (bulk modules =B) IN enclosed in a cylinder of volume V fitted with a piston of cross-section A and mass M. The piston is slightly displaced and released.Derive an expression for its time period.

A gas (bulk modules =B) IN enclosed in a cylinder of volume V fitted w

1.	A gas (bulk modules =B) IN enclosed in a cylinder of volume V fitted with a piston of cross-section A and mass M. The piston is slightly displaced and released.Derive an expression for its time period.
Answer» Solution :`B=-V(DeltaP)/(DeltaV)` where `DeltaP=(F)/(A) and DeltaV=Ax, X=` dispacement of piston `rArr B=(-V(F)/(A))/(Ax)=(-VF)/(A^(2)x) rArr K=(F)/(x)=(BA^(2))/(V), T= 2pi SRT((m)/(k))= 2pi SQRT((M)/((BA^(2))/(V)))= 2pi sqrt((MV)/(BA^(2)))`