pattern recognition in a time series

I understand that the question I am asking seem the be somewhat related to another question which has been asked already.

But I feel that this is an entirely different question.

I have a huge (over 100K data points) time series data of the position (x, y coordinates) of an element in space. This element is vibrating randomly, and both amplitude and the frequency of vibration is random. I want to look at the vibrations which are similar and see if there is any pattern in those vibrations, are they periodic or related somehow.

I am working on a biological problem and have very little knowledge about signal processing. I can provide more details Any help would be really appreciated.

Thanks in advance!!