deletions | additions       diff --git a/subsection_Varying_the_Polarization_Time__.tex b/subsection_Varying_the_Polarization_Time__.tex  index 4d56015..164c44f 100644  --- a/subsection_Varying_the_Polarization_Time__.tex  +++ b/subsection_Varying_the_Polarization_Time__.tex 
...
\subsection{Varying the Polarization Time}  We first measured the Larmor frequency, as described in the Methods, and found a value of $1.852\pm0.018~kHz$, which is very close as the manual says that the precession frequency should be approximately 2 kHz. We expect magnetization, and therefore voltage, to change exponentially with changing polarization time according to Equation~\ref{eq:growthrate} \cite{TeachSpin}. By plotting data for three different times after the polarization field was no longer applied, as shown in Fig.~\ref{fig:measurepolarizationtime} and discussed in the Methods, we could fit the data to Equation~\ref{eq:growthrate} Eq.~\ref{eq:growthrate}  and obtain values for the spin-lattice relaxation time ${T_1}$, which should be the same for our three different curves. We found ${T_1}=2.15\pm0.05 s$. \subsection{Varying the Current}  We also varied current, keeping all other values constant, and measured precession frequency. We found there to be no dependence, as expected and predicted by Equation~\ref{eq:precession}. Eq.~\ref{eq:precession}.  We expect the magnetization to vary according to Equation~\ref{eq:tanh} Eq.~\ref{eq:tanh}  when we artificially increase Earth's magnetic field, using a constant polarization time (which was in this case 10 seconds), as seen in Fig.~\ref{fig:polarizationtime10s}. Our data was initially plotted against voltage, not magnetization, but Eq.~\ref{eq:tanh} allows us to find magnetization as we can calculate $\mu$ using \begin{equation}  \label{eq:mu}  \mu=\gamma\hbar\sqrt{I(I+1)}