You can use an equivalent circuit for your resonator which is a parallel L-C resonant circuit.
Such resonant circuit should also include a loss resistor , e.g. in series with the L which determines the Q of the resonant circuit. And Q determines the "line width" of the resonant circuit.
Then if you send a frequency-modulated signal through such circuit, then the response will be limiting the FM spectrum of your signal.
All details can be found in a basic textbook of RF electronics.