$4.(8$ points$)$ For the filter circuit shown below:

a$)$ Find the functional relationships between the output voltage $\backslash ($ e$\_\{$o$\}\backslash )$ and the input voltage $\backslash ($ e$\_\{$i$\}\backslash )$ at steady state $($Hint: you may use the impedance approach$)$;

b$)$ Find the steady state frequency response of the circuit;

c$)$ First plot out the magnitude and phase responses of steady state frequency response, then name the filter.

mag: