In the arrangement shown in the figure, two positive charges +Q each are fixed. Mark the correct statement(s) regarding a third charged particle q placed at the midpoint P that can be displaced along or perpendicular to the line connecting the charges.
 

The particle will oscillate or perform SHM if equilibrium is a stable one. For negative charge, equilibrium is stable if the particles are displaced along CD and unstable for displacement along AB. 

For y << a, in displaced position, net resultant force toward equilibrium position is
$$\begin{gathered} {\mathrm{F}}_{\text{res }}=2\mathrm{Fsin}\mathrm{\theta }=\frac{2q\mathrm{Q}}{4{\mathrm{\pi \epsilon }}_0\left({\mathrm{a}}^2+{\mathrm{y}}^2\right)}\times \frac{\mathrm{y}}{{\left({\mathrm{a}}^2+{\mathrm{y}}^2\right)}^{1/2}}=\frac{2q\mathrm{Qy}}{4{\mathrm{\pi \epsilon }}_0{\mathrm{a}}^3}[\mathrm{a}>>\mathrm{y}] \\ {\mathrm{F}}_{\text{res }}\propto \mathrm{y},\text{ so SHM for }\mathrm{y}<<\mathrm{a} \end{gathered}$$
For $\mathrm{y}\simeq \mathrm{a}$, there would be restoring force, but F is not proportional to y. So there is oscillatory motion but not SHM.