A postscript to this thread, which might be of interest to some:
Those who have tested their vehicles on my multi-post rig will know that I assess each set-up using a "Performance Index" (PI), which is a cost function that weights & puts together response parameters that I believe affect the mechanical performance of a race vehicle. The idea is that a minimum value of PI represents the "best" mechanical set-up compromise.
Before TMD's were banned I was invited by one F1 team to help to optimize a TMD attached to the nose bulkhead using their multi-post rig & trial TMD hardware. The test was somewhat inconclusive, so I spent some time after the test modelling the vehicle, complete with TMD, playing with device parameters. I assessed the various parameter selections by carrying out a "rig test" with each model, processing the results in the same way as I would with a real vehicle. A summary of the results is shown here.
The plot requires some explanation. Each point corresponds to a run identified in the panel shown on the left. The run identifier refers to "PDA" (an acronym meaning Pitch Dynamic Absorber, I recall), & four parameters. The parameters were Mass (kg), Position (% wheelbase aft of the front axle), TMD natural frequency (Hz) and TMD damping ratio (% of critical). Quite clearly the "best" compromise, by my prejudices, was achieved with the natural frequency set to 7 Hz.
The result was a surprise both to me & the team, because we had assumed that the ideal natural frequency would be close to that of the pitch mode, which was around 9.5 Hz. Track tests demonstrated the model result to be correct.
The result was satisfying for me, of course, but it did demonstrate that the "obvious" solution for mechanical set-up is not always the correct one. It was the reason I suggested in an earlier post that Ferrari's claim that TMD's didn't work with Bridgestone tyres was probably because they had not tuned their version of the device to the correct frequency.