A particle of mass \(M\) and charge \(q\) is at rest at the mid point between two other fixed similar charges each of magnitude \(Q\) placed a distance \(2 d\) apart. The system is collinear as shown in the figure. The particle is now displaced by a small amount \(x(x< < d)\) along the joining the two charges and is left to itself. It will now oscillate about the mean position with a time period \(\left(\varepsilon_{0}=\right.\) permittivity of free space)

1. A \(2 \sqrt{\frac{\pi^{3} M \varepsilon_{0} d}{Q q}}\)
2. B \(2 \sqrt{\frac{\pi^{2} M \varepsilon_{0} d^{3}}{Q q}}\)
3. C \(2 \sqrt{\frac{\pi^{3} M \varepsilon_{0} d^{3}}{Q q}}\)
4. D \(2 \sqrt{\frac{\pi^{3} M \varepsilon_{0}}{Q q d^{3}}}\)