An air chamber of volume V has a neck area of cross section a into which a ball of mass m just fits and can move up and down without any friction (Fig.14.27). Show that when the ball is pressed down a little and released , it executes SHM. Obtain an expression for the time period of oscillations assuming pressure-volume variations of air to be isothermal [see Fig. 14.27].

Explanation

`T=2pisqrt((Vm)/(Ba^(2)))` where B is the bulk modulus of air. For isothermal changes B=P.