The circuit shown below is a coupled LC oscillator. $V_{IN}$ is an AC voltage represented by $V_{IN}(j)$ and $V_{Ou}(j)$ represents the output voltage. Find the network function $N(j)$ such that:

Vout$(j)=N(j)Vin(j)$

mint: mere are a number of different approaches to this problem. If you get stuck, try using a voltage divider relation, express $V_{\text{O}\text{u}\text{T}}(j)$ in terms of $V_{C_2}(j)($the voltage across $C_2)$ and again by a voltage divider relation, express $V_{CI}(j)$ in terms of the $V_{IN}(j).$