How is the waveform of an electromagnetic radiation detected and generated by a resonator (like in FM Radios)? We know that a resonator consists of an inductor and capacitor. And we also know that tuning them in a specific way will get an Electromagnetic radiation detected with similar characteristics. But when the frequency of the original EM changes how do we detect the change(Like In the FM Radios, the frequency changes but still the same wave is detected)? How and Why? 
 A: A pure sine wave RF signal does not carry any information and an ideal resonant circuit would not be able to receive information.
In order to pass some information with an RF carrier, it has to be modulated somehow.
When a carrier is modulated, regardless of the modulation method (AM, FM, etc.), it is not a pure sine wave any more - it contains a band of frequencies centered around the carrier frequency, corresponding to the band of frequencies present in the modulating signal, which could be a single tone or a continuous range of frequencies, associated with a speech. 
So, a single spectral line, corresponding to a carrier sine wave, is transformed into a relatively wide band of frequencies. We can say that a modulated carrier has some bandwidth.
In order to receive a modulated signal, the resonator of a receiver has to have a similar bandwidth or a relatively wide resonant peak. If the peak was too narrow, part (high frequencies) of the useful signal would be cut off. If the peak was too wide, the receiver could pick up frequencies belonging to other radio stations.     
A: In an fm radio the resonator you are most likely referring to has the purpose of removing out-of-band noise and is not part of the "detection" process. Detection in an fm radio is done after that band-pass filter, i.e, resonator, by converting the frequency modulation to amplitude modulation. This is done by a differentiator and an envelope detector (diode+capacitor).
