Consider an RL circuit (a resistor, $R$, and inductor, $L$, in series with a voltage source) with a sinusoidally varying voltage source ($V(t) = V_0 \sin (\omega t)$). Find the current as a function of time, $I(t)$. That is, determine both the transient response $I_H$ and the persistent result, $I_p$.
For this first attempt, use what you know about differential equations. Remember to solve the homogenous and particular problem!
Sketch the resulting current. How might you control the transient response (make it short!) to ensure it is a small effect compared to the desired persistent response?