How does the inductor have an initial condition in this circuit?
The circuit you have is this:







simulate this circuit &ndash; Schematic created using CircuitLab

I have removed the component values because they are not important for this question.  

ASSUMING the switch as been in position #1 to full charge the capacitor, the voltage at the capacitor is 20V

The AC voltage source follows \$ 100 \sqrt(2) Cos (100 t) \$, ie at t=0 has an instantaneous value of:  141.421V

The moment you throw the switch to connect the AC source to the RLC network you will have (141.421 - 20) 121.421 volts across the R-L, but how much across the inductor? Remember that for DC an inductor is a short circuit and for infinite frequency the inductor is open-circuit. Likewise remember on of the fundamental equations of an inductor:  \$V = L\frac{d I }{d t}\$ as a result the inductor appears as an open-circuit, initially and thus all 121.421V appears across the inductor and the inductor's current is 0