Two particles A and B, each carrying a charge Q are held fixed

Two particles $A$ and $B$, each carrying a charge $Q$ are held fixed with a separation $d$ between them. A particle $C$ having mass $m$ and charge $q$ is kept at the middle point of the line $A B$.

(a) If it is displaced through a distance $x$ perpendicular to $\mathrm{AB}$, what would be the electric force experienced by it.

(b) Assuming $x

(c) Under what condition will the particle C execute simple harmonic motion if it is released after such a small displacement? Find the time period of the oscillations if these conditions are satisfied.