The charge moves towards x-axis. Let at certain instant its position from point O is x. Instantaneous resultant force acting over it is given as FR=2Fcosθ =2
qQ
4πε0(a2+x2)
x
√a2+x2
FR=
2qQ
4πε0
x
(a2+x2)3∕2
This force is not of the fom F = kx Therefore, the motion of the charge Q is oscillatory but not simple harmonic.