For the given circuit, which is in steady state
- Find the frequency $\omega_{\mathrm{o}}$ at which the magnitude of the impedance across terminals $a, b$ reaches a maximum.
- Find the impedance across $a, b$ at the frequency $\omega_{0}$.
- If $v_{\mathrm{s}}(t)=\mathrm{V} \sin \left(\omega_{\mathrm{o}} t\right)$, find $i_{\mathrm{L}}(t), i_{\mathrm{R}}(t)$