$5.$ Based on the magnetically coupled circuit below,

$1)$ Draw the equivalent circuit in the frequency$/$phasor domain, replacing each magnetically coupled coil with a self$-$inductance and a dependent source. $(8$ points$)$

$2)$ Find the input impedance $\backslash ($ Z$\_\{\backslash$text $\{$in $\}\}\backslash )$ seen from the source $(6$ points$)$

$3)$ Find $\backslash ($ v$\_\{0\}\backslash )$ in the circuit. $($express it either in frequency domain or in time domain$)(6$ points$)$