I understand this question:

4. If a pendulum completes 40 vibrations in a minute, what is its period?
The period is the time for one complete cycle, and if the pendulum takes one minute (or 60 seconds) for 40 vibrational cycles, then it must take 1.5 seconds for one complete cycle.

But I can't figure out this one:
5. Describe a vibration that is not periodic.

Please help?! Thank you!

2 answers

I am sorry I can not because if you do a Fourier transform on even a spike you can express even an impulse as a sum of periodic signals. However there are articles on non-periodic vibrations in the technical literature. I question if they are really that but anyway take a look:eg:
http://www.sciencedirect.com/science/article/pii/0022460X91905928
This might help:
http://www.slideshare.net/ahmedqadoury/periodic-and-aperiodic-sounds-2