Observing phase shift with Lissajous patterns

With the FG at $100$kHz, set the scope time base to observe 1-5 cycles. Note that signal across the capacitor lags the signal across the function generator. This phase shift can be measured as the fraction of a cycle delayed times 360$^\circ$. What is the phase shift at $100$kHz?

Now measure the phase shift by means of Lissajous figures. Switch the scope display to $xy$-mode to observe the Lissajous pattern as shown in figure below. Consult the manual for your scope to find how to select the $xy$-mode. Be sure to note the sensitivity setting of each input in your measurement. The amplitude values should be recorded in volts rather than divisions. Set the sensitivities so that the major axis of the ellipse is at an angle of about 45$^\circ$ and several divisions in length. The pattern should be centered on the screen so that the central chord of the ellipse $c$, can be measured with the vertical centerline of the scope graticule.

An easy way to perform the measurement is as follows:

$\parbox{2.0in}{\raisebox{-2.2in}{\includegraphics[height=2.0in]{FIGS/fig1.3.ps}}}$ $\parbox{3.5in}{% \begin{enumerate} \item Ground the vertical amplifi... ...simply add columns to the table from the previous Section.). \end{enumerate}% }$

Frequency, $\nu$	log$_{10}(\nu)$	$b$, V	$c$, V	$\phi=\arcsin(c/b)$
10 Hz
100 kHz

Plot the phase angle, $\phi$, vs. log frequency. Again, if you are using a computer program to plot the data, you only need to fill out the columns for $b$ and $c$.

On your plot, add the line $\phi=-\arctan(\omega\tau)$, where again $\tau = RC$, using the nominal component values. Does it agree with the data?

As before, treat $\tau$ as a parameter and fit the theoretical curve to your data. Compare the two curves, and the data. Are the results of this fit in agreement with the ones from Section 1.3? Explain the differences, if any.