Emily A Kaplan edited We_next_analyze_our_time__.tex  over 8 years ago

Commit id: a4ddcb5f0e8c528c6f05b471dfa9232b6a8c0cdb

deletions | additions      

       

\end{equation}  Thus the plot of $\frac{\delta t}{\delta \omega}$ versus ratio number should look like a horizontal line. From this line we can determine a conversion factor between frequency and time.   We then plot the ratios in a very specific way- they are plotted chronologically as we passed through our frequency scan. Ratio A corresponds to $\frac{t_{2}-t_{1}}{\omega_{2}-\omega_{1}}$, B corresponds to $\frac{t_{3}-t_{2}}{\omega_{3}-\omega_{2}}$, etc, so we have five ratios for our six peaks. By plotting the ratios in this way, any drift or non-linearity in the frequency scan can be inferred by observing the slope of the values of the ratios A, B, C, D, and E when plotted against the order they came in the frequency scan. There is clearly a slope to the ratios, an example of which is seen in Fig~\ref{fig:Ratios}, indicating that our frequency scan was nonlinear. We could improve it in the future by doing a more time-intensive fit to the frequency scan.