We measured the Q of the fundamental (~106 Hz) mode of the Taiwan cantilever in two ways. First, we used Nic's active steady-state method, and then we did a traditional ringdown. The results seem to agree, but the precision of the first method is much better due to the dynamic range of the readout for this mode: the motion becomes nonlinear at an amplitude only a few times greater than the background excitation level. Over a ~4-hr average, the loss is measured to be 1.45 x 10-6 ± 2.9 x 10-7, giving a Q of ~6.9 x 105.
Here is a plot of the instantaneous phi from the calibrated control signal. This data has already been fed through a ~1-hr lowpass, and then the data from the initial settling time has been truncated away. The mean and standard deviation of the rest of the points are what is reported.
After this measurement was made, we shut off the servo and allowed the mode to ring down. Here is that ringdown, along with a predicted range of theoretical curves using the result from above. As you can see, they are fairly consistent with what is measured, considering that the system quickly reaches a regime where it is excited by the environment (that is, only the initial part of the ringdown, where the agreement is good, is very trustworthy).
This Q is a couple orders of magnitude lower than what is expected for this mode at this temperature, but it is also only a factor of 2-3 worse than the best measurements using a similar apparatus at Glasgow (to my knowledge).
It bugs me that we don't seem to have any information about what steel looks like at low temperatures. Given my COMSOL strain energy modeling, the energy ratio for this mode is about 3 x 10-4, so this could be explained by clamp loss if the steel Q is as low as a few hundred. I'm looking into other modes to try and support or refute this hypothesis; since different modes have different energy ratios, we may be able to see what's going on. In parallel, I'm asking Matt and others to find out what is really known about cryogenic steel.