Understanding First Order Circuits: DC vs. AC

[edsys89]

Hi, I'm confused with the solution given for this practice problem.
All of these components are said to be in parallel, yet the current is worked out only across the resistors. I thought the inductor would be a short circuit to DC.
Am I looking at this backwards, is it modelling the inductor charging up?

 

[jegues]

Hi, I'm confused with the solution given for this practice problem.
All of these components are said to be in parallel, yet the current is worked out only across the resistors. I thought the inductor would be a short circuit to DC.
Am I looking at this backwards, is it modelling the inductor charging up?

The sole fact that are you given Vo(t) = 2V implies that there must be current running through the other branch of resistance because there is voltage across it. (They are in parallel) Since this current isn't identical to the current in the other resistor branch, by KCL some of it must be flowing through the inductor.

This is enough to conclude that it's not being shorted out by the inductor.