In this experiment we studied pendulum motion in a non-uniformly accelerating reference frame. Special notes: Prof Goldman specifically requested to not have "100" sig figs, put font on figure axes in readable size, and don't put grids on plots!
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\usepackage{blindtext}
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\begin{document}
\title{Phys3201 Template GT}
\author{A. Partner, B. Partner, and C. Partner}
\date{\today}
\maketitle
\begin{abstract}
In this experiment we studied pendulum motion in a non-uniformly accelerating reference frame. \textbf{Special notes:} Prof Goldman specifically requested to not have ``100" sig figs, put font on figure axes in readable size, and don't put grids on plots!
\end{abstract}
\section{Introduction}
Motivate why you chose the problem that you did. Why is it interesting?
\blindtext %delete this line
\section{Background}
Give a brief summary of the physical theory, include any equations necessary, and cite any references you want to include. Here is how you insert an equation. According to
references~\cite{melissinos, Cyr, Wiki} the dependence of interest is given
by
\begin{gather*}
\mathcal{L} = \frac{1}{2} m \ell^2 ( \dot{\theta}+\dot{\phi}_0)^2 - m g_e(t) \ell \cos(\theta)\\
\\
m\ell^2 (\ddot{\theta} + \ddot{\phi}_0) = mg_e\ell\sin(\theta)\\
\end{gather*}
\begin{equation}
\ddot{\phi}(t) = -\frac{g_e(t)}{\ell} \sin\left(\phi(t)-\phi_0(t)\right)
\label{Eq:equation1} %the label lets you refer to the equation later
\end{equation}
\begin{figure}[!h]
\centering
\includegraphics[width=.8\textwidth]{pendulum.jpg}
\caption{Pendulum that starts at rest in an accelerating frame. If the acceleration is not constant then the apparent vertical, and thus $\phi_0$ will change with time}
\end{figure}
\blindtext %delete this line
\section{Methods}
Give a schematic of the experimental setup(s) used in the experiment (see
figure~\ref{fig:samplesetup}). Give the description of abbreviations
either in the figure caption or in the text. Write a description of what is
going on.
%\begin{figure}[ht]
% read manual to see what [ht] means and for other possible options
% \centering \includegraphics[width=0.8\columnwidth]{sr_setup}
% note that in above figure file name, "sr_setup",
% the file extension is missing. LaTeX is smart enough to find
% apropriate one (i.e. pdf, png, etc.)
% You can add this extention yourself as it seen below
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%\includegraphics[width=1.0\columnwidth]{sr_setup.pdf}
% \caption{
% \label{fig:samplesetup} % spaces are big no-no withing labels
% things like fig: are optional in the label but it helps
% to orient yourself when you have multiple figures,
% equations and tables
% Every figure MUST have a caption.
% }
%\end{figure}
and eventually arrived to the
balanced photodiode as seen in the figure~\ref{fig:samplesetup}.
\section{Results}
In this section you will need to show your experimental results. Use tables and
graphs when it is possible. Table~\ref{tbl:bins} is an example.
\begin{table}[ht]
\begin{center}
\caption{Every table needs a caption.}
\label{tbl:bins} % spaces are big no-no withing labels
\begin{tabular}{|cc|}
\hline
\multicolumn{1}{|c}{$x$ (m)} & \multicolumn{1}{c|}{$V$ (V)} \\
\hline
0.0044151 & 0.0030871 \\
0.0021633 & 0.0021343 \\
0.0003600 & 0.0018642 \\
0.0023831 & 0.0013287 \\
\hline
\end{tabular}
\end{center}
\end{table}
Analysis of equation~\ref{eq:equation1} shows ...
\blindtext
\begin{figure}
\centering
\includegraphics[width=.7\textwidth]{tanh_vs_const_1.png}
\caption{Hyperbolic tangent acceleration vs immediate constant acceleration. The slow approach to the same asymptotic value of 2 meters per second per second induces a lag in the oscillation and also diminishes the amplitude of oscillation.}
\end{figure}
For example, it is easy to conclude that the
experiment and theory match each other rather well if you look at
Fig.~\ref{fig:samplesetup} and Fig.~\ref{fig:exp_plots}.
\section{Conclusions}
Here you briefly summarize your findings. Did you learn any new physics? Was everything as expected?
\blindtext
\section{Future Work}
Since you had limited time to work on this project, what questions are left outstanding? What would be your next steps?
\blindtext
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% References section will be created automatically
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\bibitem{melissinos}
A.~C. Melissinos and J. Napolitano, \textit{Experiments in Modern Physics},
(Academic Press, New York, 2003).
\bibitem{Cyr}
N.\ Cyr, M.\ T$\hat{e}$tu, and M.\ Breton,
% "All-optical microwave frequency standard: a proposal,"
IEEE Trans.\ Instrum.\ Meas.\ \textbf{42}, 640 (1993).
\bibitem{Wiki} \emph{Expected value}, available at
\texttt{http://en.wikipedia.org/wiki/Expected\_value}.
\end{thebibliography}
\end{document}