$W_{e}+W_{g}=\frac{1}{2} m v^{2}$

We have work done by electrostatic force as

$W_{e}=q E l \sin \theta$

and work done by the gravitational force as

$W_{g}=m g(l-l \cos \theta)$

Thus we get

$q E l \sin \theta+m g(l-l \cos \theta)=\frac{1}{2} m v^{2}$

Thus we get

$m g \sin \theta+m g l-m g l \cos \theta=\frac{1}{2} m v^{2}$

as $\theta=45^{\circ},$ we get

$m g l=\frac{1}{2} m v^{2}$

also as $v=\omega l$

we get

$\omega=\sqrt{\frac{2 g}{l}}$