Two identical metal plates with area A and mass m are kept separated by help of three insulating springs as shown in the Figure. The equilibrium separation between the plates is `d_(0) (gt gt sqrt(A))` and force constant of each spring is K. When a constant voltage source having emf V is connected to the plates, the equilibrium separation changes to d. Assume that the lower plate is fixed and the upper plate is free to move.
(a) Find V in terms of given parameters.
(b) If the upper disc is slightly displaced from its equilibrium position and released, calculate the time period of its oscillation.

Answer

(a) `V=sqrt((6Kd^(2)(d_(0)-d))/(in_(0)A))`
(b) `T=2pi sqrt((m.d)/(3K(3d-2d_(0))))`