I dont understand when you have an AC Circuit that has a coil, capacitor and resistance. What factor will the resonant frequency change when the frequency is tripled?
I attach a resonance curve for a 160 microHenry inductance with a 160 picoFarad capacitor.
There is a series resistor of 100 ohms. The resonant frequency is 1 MHz, and sqrt(L/C) = 1000 ohms, so wL/R = Q = 10. The excitation is a swept frequency of a 1-amp current source from 300 kHz to 2 MHz. The dotted line is the phase of the circuit impedance, starting near + 90 degrees, and ending near - 90 degrees.