Physics Lab Report LaTeX Template

\documentclass[12pt]{article}
\usepackage[margin=1in]{geometry}
\usepackage{amsmath}
\usepackage{booktabs}
\usepackage{siunitx}
\usepackage{pgfplots}
\usepackage{float}
\usepackage{caption}
\usepackage{xcolor}
\usepackage{tcolorbox}
\usepackage{tikz}
\usepackage{colortbl}
\usepackage{fancyhdr}
\usepackage{hyperref}

\pgfplotsset{compat=1.18}
\sisetup{separate-uncertainty=true}
\tcbuselibrary{skins}

\definecolor{labblue}{HTML}{1D4ED8}
\definecolor{labbg}{HTML}{EFF6FF}
\definecolor{rowalt}{HTML}{F0F9FF}

\hypersetup{colorlinks=true,linkcolor=labblue}

\pagestyle{fancy}
\fancyhf{}
\fancyhead[L]{\small\textcolor{gray}{<<course_name>>}}
\fancyhead[R]{\small\textcolor{gray}{<<student_name>>}}
\fancyfoot[C]{\thepage}
\renewcommand{\headrulewidth}{0.4pt}

\newtcolorbox{labsection}[1]{
  colback=labbg, colframe=labblue!60, coltitle=white,
  fonttitle=\bfseries\small, title={#1},
  attach boxed title to top left={yshift=-2mm,xshift=6mm},
  boxed title style={colback=labblue, rounded corners},
  before skip=10pt, after skip=6pt,
}

\begin{document}

% --- Header ---
\begin{tikzpicture}[remember picture,overlay]
  \fill[labblue] (current page.north west) rectangle ([yshift=-2.2cm]current page.north east);
\end{tikzpicture}
\vspace*{0.3cm}
\begin{center}
  {\LARGE\bfseries\textcolor{white}{<<experiment_title>>}}\par
  \vspace{6pt}
  {\normalsize\textcolor{white!80}{<<course_name>>  \quad|\quad  <<student_name>>  \&  <<lab_partner>>}}\par
  \vspace{4pt}
  {\small\textcolor{white!70}{Instructor: <<instructor>> \quad Date: <<date_performed>>}}
\end{center}
\vspace{1.8cm}

\begin{labsection}{Objective}
To determine the local gravitational acceleration $g$ by measuring the period of a simple pendulum at various lengths and comparing the result with the accepted value of $g = \SI{9.81}{m/s^2}$.
\end{labsection}

\begin{labsection}{Theory}
For a simple pendulum with small angular displacement ($\theta < 15°$), the period $T$ is:
\begin{equation}
  T = 2\pi\sqrt{\frac{L}{g}}
\end{equation}
where $L$ is the length of the pendulum and $g$ is the gravitational acceleration. Squaring both sides:
\begin{equation}
  T^2 = \frac{4\pi^2}{g} L
\end{equation}
This is linear in $L$. The slope $m = 4\pi^2/g$, so $g = 4\pi^2/m$.
\end{labsection}

\begin{labsection}{Materials and Methods}
\begin{itemize}
  \item Steel bob ($m = \SI{50.0 \pm 0.1}{g}$)
  \item Nylon string ($L$ varied from \SI{0.40}{m} to \SI{1.20}{m})
  \item Digital stopwatch (resolution: \SI{0.01}{s})
  \item Meter stick (resolution: \SI{1}{mm})
\end{itemize}
For each length, 10 full oscillations were timed and repeated 3 times. The period was computed as $T = t_{10}/10$, with uncertainty from the standard deviation of trials.
\end{labsection}

\begin{labsection}{Data}
\begin{table}[H]
  \centering
  \caption{Pendulum period measurements at various lengths.}
  \label{tab:data}
  \begin{tabular}{S[table-format=1.2] S[table-format=1.3] S[table-format=1.3] S[table-format=1.3]}
    \toprule
    \rowcolor{rowalt}
    {$L$ (\si{m})} & {$T$ (\si{s})} & {$\delta T$ (\si{s})} & {$T^2$ (\si{s^2})} \\
    \midrule
    0.40 & 1.268 & 0.008 & 1.608 \\
    0.60 & 1.553 & 0.010 & 2.412 \\
    0.80 & 1.795 & 0.012 & 3.222 \\
    1.00 & 2.007 & 0.009 & 4.028 \\
    1.20 & 2.198 & 0.011 & 4.831 \\
    \bottomrule
  \end{tabular}
\end{table}
\end{labsection}

\begin{labsection}{Analysis}

\begin{figure}[H]
  \centering
  \begin{tikzpicture}
    \begin{axis}[
      width=0.75\textwidth,
      height=8cm,
      xlabel={Length $L$ (\si{m})},
      ylabel={$T^2$ (\si{s^2})},
      xmin=0.3, xmax=1.3,
      ymin=1, ymax=5.5,
      grid=major,
      legend pos=north west,
    ]
      \addplot[only marks, mark=*, mark size=2.5pt, labblue] coordinates {
        (0.40, 1.608)
        (0.60, 2.412)
        (0.80, 3.222)
        (1.00, 4.028)
        (1.20, 4.831)
      };
      \addplot[red!70!black, thick, domain=0.3:1.3] {4.028*x - 0.003};
      \legend{Data, Linear fit}
    \end{axis}
  \end{tikzpicture}
  \caption{$T^2$ vs.\ $L$ with linear regression. Slope $m = \SI{4.028 \pm 0.045}{s^2/m}$.}
  \label{fig:t2-vs-l}
\end{figure}

From the slope of the linear fit:
\[ g = \frac{4\pi^2}{m} = \frac{4\pi^2}{4.028} = \SI{9.80}{m/s^2} \]

Using standard error propagation on $g = 4\pi^2/m$:
\[ \delta g = g \cdot \frac{\delta m}{m} = 9.80 \times \frac{0.045}{4.028} = \SI{0.11}{m/s^2} \]

\textbf{Final result:} $g = \SI{9.80 \pm 0.11}{m/s^2}$
\end{labsection}

\begin{labsection}{Discussion}
Our measured value of $g = \SI{9.80 \pm 0.11}{m/s^2}$ agrees with the accepted value of \SI{9.81}{m/s^2} within experimental uncertainty. The percent error is:
\[ \%\text{error} = \frac{|9.81 - 9.80|}{9.81} \times 100\% = 0.10\% \]
Sources of systematic error include air resistance (which would increase the measured period and decrease the computed $g$) and the finite size of the bob. The small angle approximation is valid since all swings were initiated at $\theta \approx 10°$.
\end{labsection}

\begin{labsection}{Conclusion}
The gravitational acceleration was determined to be $g = \SI{9.80 \pm 0.11}{m/s^2}$, consistent with the accepted value. The linear relationship between $T^2$ and $L$ confirms the simple pendulum model for small oscillations.
\end{labsection}

\end{document}