\( L-\frac{C \cdot R_{1}^{2}}{1+\omega^{2} \cdot C^{2} \cdot\left(R_{1}+R_{2}\right)^{2}}=0 \quad \mid-L \)
\( -\frac{C \cdot R_{1}^{2}}{1+\omega^{2} \cdot C^{2} \cdot\left(R_{1}+R_{2}\right)^{2}}=-L \quad \mid(\ldots)^{-1} \)
\( -\frac{1+\omega^{2} \cdot C^{2}\left(R_{1}+R_{2}\right)^{2}}{C \cdot R_{1}^{2}}=-\frac{1}{L} \mid \cdot C \cdot R_{1}^{2} \)
\( -\frac{1+\omega^{2} \cdot C^{2}\left(R_{1}+R_{2}\right)^{2}}{1}=-\frac{1}{L} \cdot C \cdot R_{1}^{2} \mid+1 \)
\( \frac{-\omega^{2} \cdot C^{2}\left(R_{1}+R_{2}\right)^{2}}{1}=-\frac{1}{L} \cdot C \cdot R_{1}^{2}+1 \mid:-\left(C^{2} \cdot\left(R_{1}+R_{1}\right)^{2}\right. \)
\( \omega^{2}=\frac{-\frac{1}{L} \cdot C \cdot R_{1}^{2}+1}{-C^{2} \cdot\left(R_{1}+R_{2}\right)^{2}} \)
Das scheint falsch zu sein :( In der Lösung steht:
w= \( \frac{R_{1}^{2} C-L}{L C^{2}\left(R_{1}+R_{2}\right)^{2}} \)