Magnetism Exercise (08-08-2020)

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 $d_{0}$ $(<<A)$ 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.

If the upper disc is slightly displaced from its equilibrium position and released, calculate the time period of its oscillation.

If the answer come in the form of $T=\alpha \sqrt{\frac{md}{k(3d-2d_{0})}}$
Type your answer as $\alpha$ .