Confusing equivalent AC circuit (analysis)?
Proceeding via the Thevenin equivalent, nominate \$ R_2\$ as the load, and hence remove it temporarily. Also, express the components in their Laplace forms: \$L\rightarrow sL\$, and \$C\rightarrow \large \frac{1}{sC}\$; this is easier than slogging through the analysis with \$j\omega L\$ and \$\large \frac{1}{j\omega C} \$

The Thevenin voltage is then $$ V_{th}=\frac{I}{sC}$$ 

The short circuit current is: $$I_{sc}=\frac{I}{1+sR_1 C+s^2LC} $$

Hence the Thevenin impedance is: $$Z_{th}=\frac{1+sR_1 C+s^2LC}{sC} $$

Applying the Thevenin source to \$R_2\$ gives: $$U=\frac{R_2\:I}{1+sC(R_1+R_2)+s^2LC} $$

Converting this expression to a frequency response, via \$s\rightarrow j\omega\$: $$U=\frac{R_2\:I}{\left( 1-\omega^2LC\right )+j\omega C(R_1+R_2)} $$