1. Data Acquisition Overview 1 Using LabVIEW to acquire, analyze and record data

2. Data Collection One shot vs. time Using the while loop Using the DAQ for timing 2

3. DAQ set up for both Choose RSE or differential, usually the latter Choose voltage range to match your expected inputs 3

4. DAQ set up for while Collect one sample DAQ set up for DAQ timing Collect N samples Put controls on the front panel for rate and number of points Timing 4

5. Saving Data Use the Write to Measurement vi For one shots or while loop control set up: Append to File One File only One header only One time column only General set up For DAQ timing: Use next available file name. 5

6. Power Spectra Use Spectral Analysis Set to power spectrum, linear Use DAQ timing Number of points must be a power of 2, N = 2 k Sampling frequency (rate) must be high enough that half the frequency, the so-called Nyquist frequency, exceeds the highest expected frequency 6 (Maximum sampling frequency for USB6009 is 48 kHz)

7. 7 Zero Offset Correct using a high pass filter Install a control for the cut-off frequency Aliasing Test for by changing the sampling frequency Other Power Spectra Issues

8. 8 Power spectra amplitudes and frequencies Use the Peak Detector vi Create controls for threshold and peak/valley Create indicators for number detected, locations and amplitudes (but see below) Wire the output of the Spectral Analysis vi to the X (input) terminal of the Peak Detector Optional: Multiply the output of the locations terminal by rate/(number of points) to convert location to frequency

9. 9 DAQ Filter Spectrum Peaks File Raw data The spectrum I think we can record peaks as well, but I haven’t done it yet. Spectral Analysis Schematic

10. 10 Data Analysis Overview What to do with your data when you’ve got it sitting in an Excel file

11. 11 Possible tasks Calibration, interpolation Deducing constants in a theory Deducing a theory Characterizing variation in material properties

12. 12 Calibration, interpolation Generally a polynomial trendline is good enough Assess the fit using R 2, which you get for free, but which isn’t as good as Standard deviation of the fit (We have not explored techniques by which we can choose a “best” k.)

13. 13 Characterization of Material Properties You can use interpolation if you are fully ignorant You can fit models if you have one If you have time, energy and intuition, you can perhaps dream up a model and assess it! We looked at the Andrade model for the viscosity of water

14. 14 Deducing Constants in a Theory Write out the theory Beat your data into a form that you can fit in Excel Find the trendline Convert back to theory Assess the result using s.

15. 15 Bernoulli Example Theory: Plot h vs. t and fit a quadratic equation. Calculate s for the fit Is s consistent with the expected errors in the data? Do the two values of C D you calculate agree with each other?

16. 16 Cooling Curve Example Theory: You need to know, measure or estimate T f. Plot ln(T-T f ) vs. t Fit a linear trendline: m = -k and b = ln(T i -T f ) Assess the fit in the original data:

17. 17 Deducing a Theory (Boyle’s Law) Plot the data and look at it

18. 18 Looks good, but what is it? It’s not linear You can make a polynomial fit, but... there’s no physics in that — not a good idea Note: p = 0 —> V —> ∞; V —> 0 —> p —> ∞. A power law might be a good thing; plot ln(p) vs. ln(V).

19. 19

20. 20 Nice trendline (which you should assess) The linear term is the exponent, looks like -1. Carry on with the hypothesis pV = constant. (We did this and I won’t do it again here.)