${F_{net}} \Rightarrow 2F\cos \theta $ $ = 2\frac{1}{{4\pi {\varepsilon _0}}}\frac{{ - qQ}}{{({a^2} + {x^2})}}$ $ \times \frac{{ x}}{{({a^2} + {x^2})^{1/2}}}$
i.e., ${F_{net}} = - \frac{1}{{4\pi {\varepsilon _0}}}.\frac{{2qQx}}{{{{({a^2} + {x^2})}^{3/2}}}}$
As the restoring force Fnet is not linear, motion will be oscillatory (with amplitude $2a$) but not simple harmonic.
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$(a)$ The size of the antenna should be comparable to signal wavelength which is unreal solution for a signal of longer wavelength.
$(b)$ Effective power radiated by a long wavelength baseband signal would be high.
$(c)$ We want to avoid mixing up signals transmitted by different transmitter simultaneously.
$(d)$ Low frequency signal can be sent to long distances by superimposing with a high frequency wave as well.
Therefore, the most suitable options will be