J. Kissel, K. Venkateswara, E. Shaw

We've processed the 1 [mHz] excitation data taken over night, and it confirms our preliminary results from yesterday that the center of mass of the beam is d = 20 [um] above the suspension point. Indeed, because we shielded most of the open end of the thermal box with Ameri-stat (as shown in yesterday's pictures), the insturment's noise floor was much better. 

Note, we've also switched from Krishna's sine-wave fitting code to just grabbing the excitation amplitude from the ASD, and obtaining a transfer function value from there,
peak amplitude [rad_{pk}] = ASD [rad_{rms}/rtHz] * sqrt(binWidth) [rtHz] * sqrt(2) [pk / rms].
Since we know the response to ground tilt should tend to unity at high frequency, as any inertial sensor, and we've not changed the excitation amplitude, the collection of peak amplitudes are normalized by the highest-frequency amplitude to obtain the (beam / ground) [rad/rad] tilt transfer function. We lose a quantitative estimate of the uncertainty with this method, but we gain simplicity/clarity and it's reasonable to say from the SNR that the estimates are good to at least 20%, if not better. See attachment. 

The adjustment masses are a distance D = ~3 [in] above the C.o.M., so the change in (d = C.o.M. w.r.t the Susp. Point) per gram of adjustment weight, dm, is

dC.o.M.    D     3.0 [in]   76.2e-3 [m]
------  = --- =  -------- = ----------- = 18.1 [um/g]
  dm       M     4.2 [kg]     4.2  [kg]

As such to achieve a minimal separation, Krishna and Eric spent the rest of the morning/early afternoon removing 1.1+/- 0.05 [g]  of mass (equal to a 19.91 [um] shift in C.o.M. down toward the Susp. Point). A separation of ~1 [um] means the rejection of horizontal acceleration is

d * M_{bar}    1e-6 [m] * 4.2 [kg]        
----------  =  -------------------- = 7e-6 [rad/m]
  I_{bar}          0.59 kg.m^2

... pretty awesome! After rebalancing, they sealed the vacuum chamber (tool tight), confirmed that the new resonant frequency is 8.8 [mHz] as expected, and headed home for Seattle. 

When Krishna returns on Monday, we'll start pulling vacuum on the tank which should take about a day. From there we tweak the balance of the beam to remain within range of the autocollimator, re-measure the C.o.M.-Sus.Point separation to confirm the awesome acceleration rejection, and begin the process of connecting the system to the aLIGO DAQ.