Andrea,
1. Find peaks of oscillations.
2. Fit an exponential to the peaks.
3. Damping is exponential coefficient. You may need to adjust to your time scale.
Your signal is clean enough that this works well. I used the Peak Detector VI with the threshold set to .05 and the width to 5. The default width is 3 but you have a bit of noise so I widened the peak a bit to reduce the chances of "detecting" multiple peaks due to noise. Note that it does get multiples at 1439, 1442, 1444.
So that I do not need to read the file every time I run, I made the Waveform Graph value default and then converted it to a control.
Lynn