Part 1
One can take a signal that would be periodic in continuous time and turn it into a signal that is not periodic in discrete time. Consider the continuous time signal $ x(t)=sin(t) $. Plotting this signal yields a smooth waveform that repeats itself with period $ T=2\pi $.
The continuous-time signal $ x(t)=sin(t) $ is periodic.
Sampling this signal at every integer time yields something altogether different.
Sampling the continuous-time signal $ x(t)=sin(t) $ at integer times yields something like this. Note that the new discrete-time function $ x[n]=sin(n) $ is not periodic. Here we have shown ten cycles of the formerly-periodic continuous time function.
The new discrete time function looks like this on its own.
The non-periodic discrete-time function $ x[n]=sin(n) $.
