Thanks a lot, Ratch!
I agree with you that I have forgotten much of the details but at the same time I was approaching the problem differently. Please have a look here. I was thinking that "initial expression" and "final expression" are equivalent; it's just that "initial expression" has been written in terms of Q_L and later it was expanded and simplified into "final expression". In other words, I wasn't really trying to derive resonant frequency; I was more of focused on trying to derive the "final expression" using "initial expression". But it looks like they aren't equivalent.Your attempt to derive the resonant frequency with resistance present in the coil tells me that you do not quite understand the principle of parallel resonance (PR).
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