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!

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

To describe a vibration that is not periodic, we need to understand the concept of periodicity. In physics, periodicity refers to a repeating pattern or cycle that occurs at regular intervals. In the context of vibrations, periodic vibrations are those that repeat the same pattern over and over again at regular time intervals.

On the other hand, a non-periodic vibration does not follow a regular pattern and lacks repetition. This means that the vibrations do not occur at regular time intervals, and the pattern of motion does not repeat itself.

To further understand this concept, consider an example of a non-periodic vibration: a car driving on a bumpy road. As the car encounters bumps, the motion of the vehicle becomes irregular and unpredictable. The vibrations produced by the car hitting each bump are not repeating at regular time intervals since the distance between each bump and the intensity of the vibrations will vary.

Another example of a non-periodic vibration is the sound produced by clapping hands. Each clap produces a unique sound, and the time intervals between each clap are inconsistent, leading to a non-periodic vibration.

In summary, a vibration that is not periodic lacks a repeating pattern and occurs irregularly without recurring at regular time intervals.