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The $LRC$ circuit above is connected to an alternating voltage $V_0\sin(\omega t)$ and the circuit run until it is in a steady state. Find or show:

1. The impedance $Z$ of the circuit.
2. The current $I(t)$ in the circuit, in terms of the givens. Be sure to define all terms used e.g. $\phi$.
3. Draw a qualitatively correct figure of $P_{\rm av}(\omega)$ (the average power as a function of $\omega$) for the oscillator if it has $Q = 10$ and a resonant frequency $\omega_0$.