Engineering Phasor circuit solving for current

[gfd43tg]

As I am trying this problem, I convert the current source to e^(j30°). I am not sure what I should do with that. I added it to the other current source that I did a source transformation on. By the way, all the components should have the same frequency as the voltage source, right? The frequency of the current source doesn't affect the impedance of the capacitors and inductors?

 

[gfd43tg]

Here is my attempt

 

[NascentOxygen]

It's a linear circuit, so you can determine Ix due to one source (with the other source "disabled"), and then determine Ix due to the second source (after "disabling" the first).

The circuit's Ix will be the sum of those two components, which you express by simply writing a "+" sign between the two above components because they are not of the same frequency.

 

[rude man]

You need to solve for each frequency separately. Convert each solution into the time domain, then add in the time domain. You can't avoid converting to the time domain separately for w1 and w2 before the final addition.

 

[gfd43tg]

Here is my attempt, I think he had a little trick going

 

[rude man]

You were clever to notice the resonances of the two L-C circuits & that there is a short circuit at each frequency. And your final answer is 100% correct! Nice work.