A wooden block performs SHM on a frictionless surface with...

Frequency or time period of SHM depends on variable forces. It does not depend on constant external force. Constant external force can only change the mean position. For example, in the given question mean position is at natural length of spring in the absence of electric field. Whereas in the presence of electric field mean position will be obtained after a compression of $x_0$. Where $x_0$ is given by or $$\begin{aligned}k x_0 & =Q E \\ x_0 & =\frac{Q E}{k} \end{aligned}$$\therefore$ Correct answer is (a). Analysis of Question (i) Question is simple. (ii) I think almost all the serious aspirants of JEE can solve this problem easily.