Unstable Equilibrium of hinged rods

I conjured up a scenario where there are two rods free to rotate about a hinge connected by their ends by spring of spring constant $k$,both their masses are $m$ and length $l$ and mass is uniformly distributed throught the length, now on the upper rod a charge $q$ is uniformly distributed and a constant horizontal electric field is switched on

$vec{E}=E_0hat{i}$

My queries are:-

1. Is the question framed correct?Will there be a static equilibrium?

2.If yes then how would $E_0$ vary
Is there only one value of $E_0$ for equilibrium,If yes,then what is it?
Or there will be a range of values of $E_0$ with varying extension in the spring?

Also

Will the system oscillate if the upper rod is given a slight angular displacement? What will be its time period?Will the spring be the one oscillating or will the entire system oscillate about the hinge?

Please help me out. Im not looking forward towards a detailed solution hints will be enough. Thanks in advance!