Two equal negative charges -q are fixed at points (0, a) and (0, - a) on the y-axis. A positive charge Q is released from rest at the point (2a, 0) on the x-axis. The charge Q will

By symmetry of problem, the components of force on Q due to charge at A and B along y-axis will cancel each other while along x-axis will add and will be along CO. Under the action of this force, charge Q will move towards O. If at any time charge  Q is at a distance x from O,

$\begin{array}{l}\mathrm{F}=2\frac{1}{4{\mathrm{\pi \epsilon }}_{\mathrm{o}}}\frac{-\mathrm{qQ}}{\left({\mathrm{a}}^2+{\mathrm{x}}^2\right)}\times \frac{\mathrm{x}}{{\left({\mathrm{a}}^2+{\mathrm{x}}^2\right)}^{1/2}}\\ \mathrm{i}.\mathrm{e}.,\mathrm{F}=-\frac{1}{4{\mathrm{\pi \epsilon }}_{\mathrm{o}}}-\frac{2\mathrm{qQx}}{{\left({\mathrm{a}}^2+{\mathrm{x}}^2\right)}^{3/2}}\end{array}$

As the restoring force F  is not linear, motion will be oscillatory (with amplitude 2a) but not simple harmonic.