I ran across a post on LLC competitor SpeedUp's website about vibrations in their test stand. The post reminded me of some similar tests I did to measure vibrations in thrust measurements.
As you might be able to tell from the picture in this post , I'm using a beam load cell to measure thrust. It has the advantages of being relatively easy to mount and requiring only one load cell. It has the disadvantage of turning the engine into a vibrating, cantilevered beam supported by the load cell. Fortunately, my data sample rate was 10kHz, so I was able to spot the low frequency ringing by comparing the thrust and chamber pressure data.
In order to determine which frequencies were caused by the test stand and which were "real", I did a hammer test. My test stand is mounted on a steel I-beam, so I turned on the DAQ system and hit the beam with a hammer. The next two charts show the raw thrust data and a FFT of thrust data. The FFT shows vibrations at 31, 33, and 85 Hz, so I can use a digital filter to remove that frequency content from my test data. I use and recommend Sigview to do plots, FFTs, and filtering.