Depending on the purpose of your analysis, you can use a variety of measurement techniques
The simplest is to detect level, e.g. sound pressure level or vibration level to quantify how much it vibrates
Next, you can register time data and calculate spectrum to see the frequency content which will tell you which part of the motion is repetitive. If you wish, you can dig into the details of time signals and look at repetition, look for nonlinearities and so on.
If you use one reference sensor and a 2nd sensor that you move, you can make operational deflection analysis and see motion patterns at repetitive frequencies
If you use multiple channels and record them all in one go, you can animate motion with time. If your transducers are of the correct type, you may integrate from vibration to position.
Here are some ramblings of mine on the subject of measurement