A small nit, so common that it must have worked its way into the EE text books. If you sample exactly at Nyquist, you will get a straight line. Of course you are reading the signal at exactly the same point in its cycle every time. The Nyquist criteria is that you must sample at GREATER THAN twice the frequency of the signal of interest. And how long you need to sample is related to how much greater the sampling rate. If you need quick results, over sample, and not at an harmonic of the signal of interest (well sometimes a harmonic, if you know what you are looking for. Optimal filters, blah blah…).
It is like over-tipping. It can pay off if you forget your new hat and the waitress runs out into the parking lot to give it to you, instead of going home with her nice new hat.