The formula for resonant frequency is given by:Thom, I believe that the resonant frequency is determined purely by L and C, per the equation you cited. R will affect the degree of damping of that resonant peak.
res. freq. = 1 / [2 * pi * sqrt (L * C) ].
I believe this is the net capacitance, but what I'm not clear on is whether the resistive load is taken into account - whether we're talking about the net capacitance as defined by the RC circuit (including the resistive load), or whether the only effect is the raw capacitive elements - without taking the "R" (resistive load) into account.
If R is very high, say 47K, that peak will be relatively large. If R is excessively low, the low pass filter formed by L and R will cause the overall frequency response to roll off before the frequency of the resonant peak is reached. If R is optimal (with respect to damping of the resonant peak, which may or may not be optimal in terms of overall system synergy), then the response will be essentially flat up to the area of resonance, and above that frequency a smooth rolloff will occur.
As you aptly stated, "'just enough' is always the best solution."
Great thread, btw!
Best regards,
-- Al