In NMR, for example, why it is not possible to excite nuclei from one spin state to another using energy of arbitrary frequency?
This is indeed the basis of modern Fourier transform NMR (the technique that all modern spectrometers use).
The molecule is irradiated with a range of frequencies and the response detected. Application of some clever maths (the Fourier transform) then allows the individual signals to be observed.
You can think of this a bit like bashing every key on a piano and recording the noise. Application of Fourier transform would then allow you to get back the sound for the individual keys.