The positive charge $Q$ is attracted by both fixed negative charges $-q$. Due to the symmetry of the setup, the vertical components of the forces cancel out, while the horizontal components add up, creating a net restoring force directed towards the origin.

The magnitude of this net force at a distance $x$ from the origin is given by the superposition of Coulomb forces: $F_{net} = \frac{2kQqx}{(x^2 + a^2)^{3/2}}$.

For a particle to execute Simple Harmonic Motion (SHM), the restoring force must be directly proportional to the displacement ($F \propto -x$). In this case, the force is proportional to $x$ only when $x \ll a$ (small oscillations). However, the charge is released at $x = 2a$, which is not small compared to $a$. Since the relationship between force and displacement is non-linear for this amplitude, the motion will be oscillatory (repetitive back and forth through the equilibrium point) but not simple harmonic.