Periodic Functions
The function $ f(t)=sin(t-T) $ is periodic, with a period of $ T=2\pi $. This means that for $ T=2n\pi $, n an integer, the function will be unchanged from when $ T=0 $.
An example of a periodic function $ f(t)=sin(t-T) $. The dashed red line represents various values of $ T $ from $ T=0 $ to $ T=2\pi $. One can see that when $ T=2\pi $, the function is unchanged.
Non-periodic Functions
A non-periodic function does not remain self-similar for all integer multiples of its period. A decaying exponential is an example of a non-periodic function. The distance between consecutive peaks does not remain constant for all values of $ x $, nor does the amplitude of consecutive peaks remain constant. Presented here is the function $ f(t)=e^{0.2t}*sin(10t) $.
An example of a non-periodic function $ f(t)=e^{0.2t}sin(10t) $.
