In the Circuit Shown Below, Let (A) Write a Node Equation at Node 1 by Summing

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In the circuit shown below, let $$\mathrm { R } _ { 1 } = 1 \Omega , \mathrm { R } _ { 2 } = 2 \Omega , \mathrm { L } = 1 \mathrm { H } , \mathrm { C } = 0.1 \mathrm {~F} , \mathrm {~V} _ { \mathrm { b } } = \mathrm { V } _ { \mathrm { o } }$$
(a) Write a node equation at node 1 by summing the currents leaving node 1 .
(b) Write a node equation at node 2 by summing the currents leaving node $2 .$
(c) Find the transfer function $\mathrm { H } ( \omega ) = \mathrm { V } _ { \mathrm { o } } / \mathrm { V } _ { \text {in } }$ .
(d) Plot the magnitude response $| H ( \omega ) |$ and find the value of $| H ( \omega ) |$ at $\omega = \infty$ .
(e) What type (LPF, HPF, BPF, BSF) of filter is this?