I've been working with phasors and s-domain analysis for a little bit
now. My mathematical skills aren't the best and I'm not seeing how
these two analysis techniques are linked together.

I analyzed the simple RC circuit here: http://img76.imageshack.us/img76/4459/rcfq0.jpg

Is my math at the end correct in finding the sinusoidal response? There should be an s^3 term in the denominator?

How do we manage to find frequency response so much easier using Eulers formulas?

I'm not asking how to do it with Euler's, I'm asking to understand intuitively how the two are linked. Is there a certain proof out there that is commonly used to make this "click" ?

Thanks.

I analyzed the simple RC circuit here: http://img76.imageshack.us/img76/4459/rcfq0.jpg

Is my math at the end correct in finding the sinusoidal response? There should be an s^3 term in the denominator?

How do we manage to find frequency response so much easier using Eulers formulas?

I'm not asking how to do it with Euler's, I'm asking to understand intuitively how the two are linked. Is there a certain proof out there that is commonly used to make this "click" ?

Thanks.