This morning, I manually performed ringdown measurements for two elastic oscillation modes (23.602 kHz and 23.668 kHz) found at ETMX. Each mode was measured 10 times.
Figure 1 and Figure 2 show example ringdown plots for each mode, respectively.
I asked Marc-san to calculate the Q-values from these measurements.
I evaluated the decay time of the ringdown data. After taking an RMS with 32 Hz sampling and assigning an error bar with a constant and a scaling term, I fitted to the following function:
![\begin{align*}f(t) = \sqrt{\left(A\cdot \left[ \theta(t_0-t) +\theta(t-t_0)\cdot e^{-\frac{t-t_0}{\tau}}\right]\right)^2 + B^2 }\end{align*}](https://texclip.marutank.net/render.php/texclip20251204230405.png?s=%5Cbegin%7Balign*%7D%0Af(t)%20%3D%20%5Csqrt%7B%5Cleft(A%5Ccdot%20%5Cleft%5B%20%5Ctheta(t_0-t)%20%2B%5Ctheta(t-t_0)%5Ccdot%20e%5E%7B-%5Cfrac%7Bt-t_0%7D%7B%5Ctau%7D%7D%5Cright%5D%5Cright)%5E2%20%2B%20B%5E2%20%7D%0A%5Cend%7Balign*%7D&f=c&r=150&m=p&b=f&k=f)
where A, B, τ, and t0 are constants, and θ(*) is the step function. Please see the plots.
K1:MIR-AS_PDA1_RF17_I_OUT
The same analysis for K1:MIR-AS_PDA1_RF17_Q_OUT
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[[Fit Statistics]]
# fitting method = Nelder-Mead
# function evals = 134
# data points = 640
# variables = 4
chi-square = 631.154009
reduced chi-square = 0.99238052
Akaike info crit = -0.90769389
Bayesian info crit = 16.9381788
R-squared = 0.99930151
[[Variables]]
A: 2.59188636 +/- 0.00312947 (0.12%) (init = 2.590804)
tau: 0.65404324 +/- 0.00485124 (0.74%) (init = 0.7)
t0: 4.35257830 +/- 0.00380638 (0.09%) (init = 4.34)
B: 0.27152901 +/- 0.00100363 (0.37%) (init = 0.2712595)
[[Correlations]] (unreported correlations are < 0.100)
C(tau, t0) = -0.7595
C(A, t0) = -0.2075
C(tau, B) = -0.1498I performed the fitting for all files of the 23.602kHz ringdown.
The result was Q = 4.91 x10^4
I performed the fitting for all files of the 23.668kHz ringdown.
The result was Q = 2.5 x10^4
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