Could someone please help me solve this given problem:



Here's my current approach:



I think I did it correctly? But not too sure about finding the output for a very small complex frequency and very large complex frequency.

Does this mean that for when t = ∞, the capacitor becomes a short? Then I would just go with the same approach as in my above solution?

For t = -∞, I'm not exactly sure what happens. Do the capacitors become open circuits??

If someone could please point me in the right direction or help me with suggestions, I would really appreciate it. I am just really confused right now...

 

You need to find I through L and not through Z.

Calculate R//C and then use the current divider rule to find the current through L.

 

I guess very small freq means capacitor is open and very large freq means the inductor is open. But that's just ideal case.