Physics - SHM Question with Solution | TestHub

Component of force on charge of $+Q$ at $P$, along $x$-axis, $\begin{array}{rl}{F}_x& =\frac{2Qq}{4\pi {\epsilon }_0\left(a^2+x^2\right)}\times \frac{x}{\sqrt{a^2+x^2}}\\ & =\frac{2Qqx}{4\pi {\epsilon }_0\left(a^2+x^2\right)}\times \frac{x}{\sqrt{a^2+x^2}}\\ & =\frac{2Qqx}{4\pi {\epsilon }_0{\left(a^2+x^2\right)}^{3/2}}\end{array}$Which is not directly proportional to $x$. So, motion is oscillatory but not SHM.