deletions | additions       diff --git a/textit_Kept_polarization_time_constant__.tex b/textit_Kept_polarization_time_constant__.tex  index 5f6709f..bb0601f 100644  --- a/textit_Kept_polarization_time_constant__.tex  +++ b/textit_Kept_polarization_time_constant__.tex 
...
%-Kept polarization time constant at 5s, varied current, measured amplitude at three peaks of the precession data corresponding to t=0 ms, t=50 ms, and t=100 ms, corresponding to time after the polarization field is no longer applied. We then fit data to eqn (something) which tells us relationship between time and magnetization.\\  %-Kept current constant and varied polarization, measuring amplitude and therefore magnetization. We could see find our saturation polarization time this way, as the amplitude eventually stops increasing.\\  %-Then kept polarization time constant at 10s (saturation) and varied current, recording amplitude. In this way we can find dependence of magnetization on magnetic field.\\}  We could vary the polarization time and the magnetic field (through varying the current) to see their effects (if any) on precession frequency and amplitude (and therefore magnetization). In order to measure the frequency, we adjusted the scale of the oscilloscope so that we had at least 10 (but not many more) periods on the oscilloscope display, and measured the frequency for 10 cycles. We used frequency the oscilloscope measured for 10 cycles to determine the frequency of one cycle- the Larmor precession frequency. In order to measure amplitude, we chose to measure the amplitudes of three cycles whose peaks fell on the points t=0 ms, t=50 ms, and t=100 ms, with t=0 corresponding to the time when the polarization field is no longer applied, applied and any artifacts from the electronics have died out,  and measured the amplitude of the peak at each of those points as they were points which we could find easily on the oscilloscope. For all the data we took, we plotted the shape of the amplitude vs (whichever variable we were determining dependence upon) separately for each of the three points, as they should all tell us the same information but fall at different times in the data. \\ We first kept the polarization time constant at 4s and varied the current from 0.5A to 3.0A, corresponding to varying field from 7.5 mT to 45 mT, in order to determine the dependence of precession frequency upon polarization field. We found there to be no dependence, as predicted by Equation ~\ref{eq:precession}, and we found the precession frequency to be $1.852 kHz \pm 0.018 kHz$. We then kept the polarization time constant at 5s and varied the field form 7.5 mT to 45 mT, measuring the amplitude of the precession data using the method described above. We then fit the data to a linear fit, so we can determine the relationship between polarization time and magnetization. We then kept the field constant at 45 mT and varied polarization time, measuring amplitude and therefore magnetization. We then fit the data to Eqn.~\ref{eq:growthrate} to find the rate of polarization of the water molecules. We again kept field constant at 45 mT and varied the polarization time, measuring the amplitude to find the time at which saturation occurs. We could then record the amplitude seen when keeping the polarization at the saturation time (\sim{10}s, see Figure~\ref{fig:measurepolarizationtime}) and varying the current. In this way, we can find the dependence of magnetization on magnetic field.