Well there seem to be no comments here but at least I think that this is an interesting and easy to understand explanation of the concept used to acquire the decay signal.

So I assume you can identify different elements in the sample by examining the spectrum of the resulting decay and looking for specific decay/rotation frequencies? Does this work only with elements or would molecules react in the same way?

Hey thrash, good question! In NMR, the nuclei we manipulate are almost always bound into molecules.

Many elements have isotopes that are 'NMR active' (13C, 15N, 31P, 19F, even 2H) that we can measure, and yes, they show up at different frequencies. A super cool experiment to do on PPM's is to acquire a decay from something with both 1H and 19F: because their frequencies are so close together, you get a trippy, easily identifiable beat pattern in the time-domain signal.