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\documentclass[12pt,a4paper]{article}
\usepackage{lmodern}
\usepackage{microtype}
\usepackage[utf8]{inputenc}
\usepackage{amsmath,amssymb}
\usepackage{siunitx}
\usepackage{booktabs}
\usepackage{geometry}
\geometry{margin=2.5cm}
\title{Lab Report: Measurement of Gravitational Acceleration}
\author{Student Name \\ Partner Name}
\date{\today}
\begin{document}
\maketitle
\section{Objective}
Determine the local gravitational acceleration $g$ using a simple pendulum,
and compare the result to the accepted value of
$g = \SI{9.81}{m/s^2}$.
\section{Theory}
For small oscillations, the period $T$ of a simple pendulum of length $L$ is:
\[
T = 2\pi\sqrt{\frac{L}{g}}
\]
Solving for $g$:
\[
g = \frac{4\pi^2 L}{T^2}
\]
\section{Data}
\begin{table}[h]
\centering
\begin{tabular}{ccc}
\toprule
Trial & Length $L$ (m) & Period $T$ (s) \\
\midrule
1 & 0.500 & 1.421 \\
2 & 0.500 & 1.419 \\
3 & 0.500 & 1.423 \\
\midrule
Mean & 0.500 & 1.421 \\
\bottomrule
\end{tabular}
\caption{Pendulum period measurements at fixed length $L = \SI{0.500}{m}$.}
\end{table}
\section{Results}
Using $L = \SI{0.500}{m}$ and $T = \SI{1.421}{s}$:
\[
g = \frac{4\pi^2 \times 0.500}{(1.421)^2} = \SI{9.78}{m/s^2}
\]
\section{Error Analysis}
The percentage error relative to the accepted value is:
\[
\text{error} = \frac{|9.78 - 9.81|}{9.81} \times 100\% = 0.31\%
\]
\section{Conclusion}
The measured value $g = \SI{9.78}{m/s^2}$ agrees with the accepted value
to within experimental uncertainty. Main sources of error: air resistance,
timing reaction delay, and non-zero amplitude.
\end{document}