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% paper written by Claude AI | ||
\begin{document} | ||
\maketitle | ||
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\begin{abstract} | ||
This paper provides a brief overview of the simple harmonic oscillator, | ||
focusing on its mathematical description and physical significance. We discuss | ||
the fundamental equation of motion and its solution, demonstrating why this | ||
system serves as a cornerstone model in physics. | ||
\end{abstract} | ||
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\section{Introduction} | ||
The simple harmonic oscillator is one of the most fundamental models in physics. | ||
Its applications range from the motion of pendulums to the behavior of atoms | ||
in crystal lattices \citep{feynman1963}. | ||
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\section{Mathematical Description} | ||
The equation of motion for a simple harmonic oscillator is given by: | ||
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\begin{equation} | ||
\frac{d^2x}{dt^2} + \omega^2x = 0 | ||
\end{equation} | ||
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where $\omega$ is the angular frequency of oscillation. The general solution | ||
to this equation is: | ||
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\begin{equation} | ||
x(t) = A\cos(\omega t + \phi) | ||
\end{equation} | ||
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where $A$ is the amplitude and $\phi$ is the phase constant | ||
\citep{goldstein2002}. | ||
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\bibliography{references} | ||
\bibliographystyle{plainnat} | ||
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\end{document} |
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% references.bib | ||
@book{feynman1963, | ||
author = {Feynman, Richard P. and Leighton, Robert B. and Sands, Matthew}, | ||
title = {The Feynman Lectures on Physics}, | ||
year = {1963}, | ||
publisher = {Addison-Wesley}, | ||
address = {Reading, MA} | ||
} | ||
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@book{goldstein2002, | ||
author = {Goldstein, Herbert and Poole, Charles and Safko, John}, | ||
title = {Classical Mechanics}, | ||
year = {2002}, | ||
edition = {3rd}, | ||
publisher = {Addison Wesley}, | ||
address = {San Francisco} | ||
} |
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name: LATEX | ||
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on: | ||
push | ||
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jobs: | ||
build_paper: | ||
runs-on: ubuntu-latest | ||
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permissions: | ||
contents: write | ||
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steps: | ||
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- name: Checkout repository | ||
uses: actions/checkout@v4 | ||
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- name: Cat action | ||
run: | | ||
cat ./actions/latex/action.yml | ||
#- name: Build LaTeX document | ||
# uses: ./actions/latex | ||
# with: | ||
# paper: ".github/hello-paper/main.tex" | ||
#secrets: | ||
# GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }} | ||
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#- name: Upload build artifacts | ||
# uses: actions/upload-artifact@v4 | ||
# with: | ||
# name: latex-build-${{ github.sha }} | ||
# path: publish/ | ||
# retention-days: 7 |
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