Part 1
I'll use the signal that I picked for the last homework to demonstrate the sampling rate idea. My signal was tan(t). If you sample this function at a rate of $ pi $, every sample will be identical, as long as it's not shifted by $ \frac{\pi}{2} $ as $ \tan(\frac{\pi}{2}+n*\pi) $ for any integer n is undefined.
However, if you sample this function with a period of anything OTHER than $ \pi $ then you get random dots all over the place.
