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Message ID: 1314     Entry time: Tue Aug 27 15:45:28 2013
Author: Evan 
Type: DailyProgress 
Category: Seismic 
Subject: Resonances of the seismic isolation stack 

[Tara, Koji, Evan]

On Friday when the vacuum chamber was open, we took some impulse response measurements of the seismic isolation stack. We used a HeNe laser and a PDA100A as a shadow sensor for recording the responses.

The measurement setups were as follows:

  1. With the shadow sensor positioned so as to register vertical motion of the top surface of the seismic stack, Tara poked the top of the cavity mount.
  2. With the shadow sensor positioned so as to register vertical motion of the top surface of the seismic stack, Tara poked the top surface of the seismic stack near the end of the stack.
  3. With the shadow sensor positioned so as to register vertical motion of the top surface of the seismic stack, Tara poked the right side of the seismic stack near the end of the stack.
  4. With the shadow sensor positioned so as to register horizontal motion of the transmission corner of the seismic stack, Tara poked the left side of the seismic stack near the end of the stack.
  5. With the shadow sensor positioned so as to register horizontal motion of the transmission corner of the seismic stack, Tara poked the front of the seismic stack near the end of the stack.

For each setup, two ringdows were taken with the scope AC coupled (we'll call them measurements A and B).

I used scipy.optimize.curve_fit to fit each ringdown to the sum of two damped harmonic oscillators:

V(t) =
\theta(t-b) \left\{a_1 \mathrm{e}^{-\gamma_1 (t-b)} \sin\left[2\pi f_1 (t - b) + \phi_1\right] + a_2 \mathrm{e}^{-\gamma_2 (t-b)}
\sin\left[2\pi f_2 (t - b) + \phi_2\right]\right\}

where θ is the Heaviside step function. In the table below I've collected the fitted frequencies and Q factors. In the first attachment I've plotted the ringdowns, their Fourier transforms (with no windowing—very crude, but it is only intended as a very rough guide), and the fits (in red).

Setup Meas. A Meas. B
1

f1 = 10.5 Hz; Q1 = 0.2

f2 = 7.2 Hz; Q2 = 0.3

f1 = 3.6 Hz; Q1 = 0.16

f2 = 10.4 Hz; Q2 = 0.2

2

f1 = 10.4 Hz, Q1 = 0.2

f2 = 7.0 Hz; Q2 = 0.12

f1 = 10.5 Hz; Q1 = 0.3

f2 = 6.7 Hz; Q2 = 0.08

3

f1 = 3.6 Hz; Q1 = 0.4

f2 = 7.3 Hz; Q2 = 0.3

f1 = 3.6 Hz; Q1 = 0.4

f2 = 7.3 Hz; Q2 = 0.4

4

f1 = 3.5 Hz; Q1 = 0.5

f2 = 3.9 Hz; Q2 = 0.3

f1 = 3.5 Hz; Q1 = 0.6

f2 = 4.4 Hz; Q2 = 0.17

5

f1 = 4.2 Hz; Q1 = 0.5

f2 = 6 Hz; Q2 = 0.4

f1 = 3.4 Hz; Q1 = 0.2

f2 = 4.3 Hz; Q2 = 0.6

I haven't assigned error bars here because I think I may be overfitting; the amplitude and phase parameters and the offset parameter have huge uncertainties (many times the nominal value). However, by eye the fits of the ringdowns appear to be pretty good, and so I am inclined to believe the fitted frequency values.

Attachment 1: ringdowns_and_ffts.pdf  1.007 MB  Uploaded Tue Aug 27 16:54:10 2013  | Hide | Hide all
ringdowns_and_ffts.pdf ringdowns_and_ffts.pdf ringdowns_and_ffts.pdf ringdowns_and_ffts.pdf ringdowns_and_ffts.pdf ringdowns_and_ffts.pdf ringdowns_and_ffts.pdf ringdowns_and_ffts.pdf
Attachment 2: ringdown_data.zip  91 kB  Uploaded Tue Aug 27 16:54:37 2013
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