Lab report for Period of a Pendulum Lab
\begin
Opdag hvorfor 18 millioner mennesker verden rundt stoler på Overleaf med deres arbejde.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% _______ _ _ _____
% |__ __| | | |/ ____|
% | | | |__| | (___
% | | | __ |\___ \
% | | | | | |____) |
% |_| |_| |_|_____/
%
% _ ____
% | | /\ | _ \
% | | / \ | |_) |
% | | / /\ \ | _ <
% | |____ / ____ \| |_) |
% |______/_/ \_\____/
%
% _______ ______ __ __ _____ _ _______ ______
%|__ __| ____| \/ | __ \| | /\|__ __| ____|
% | | | |__ | \ / | |__) | | / \ | | | |__
% | | | __| | |\/| | ___/| | / /\ \ | | | __|
% | | | |____| | | | | | |____ / ____ \| | | |____
% |_| |______|_| |_|_| |______/_/ \_\_| |______|
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% DONT CHANGE ANYTHING BEFORE THE "TITLE" SECTION.%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\documentclass{article} % Don't change this
% _____ _____ _ __ _____ ______ _____
%| __ \ /\ / ____| |/ / /\ / ____| ____|/ ____|
%| |__) / \ | | | ' / / \ | | __| |__ | (___
%| ___/ /\ \| | | < / /\ \| | |_ | __| \___ \
%| | / ____ \ |____| . \ / ____ \ |__| | |____ ____) |
%|_| /_/ \_\_____|_|\_\/_/ \_\_____|______|_____/
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage[english]{babel}
\usepackage[utf8]{inputenc}
\usepackage[margin=1.5in]{geometry}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage[usenames,dvipsnames]{xcolor}
\usepackage{graphicx}
\usepackage[siunitx]{circuitikz}
\usepackage{tikz}
\usepackage[colorinlistoftodos, color=orange!50]{todonotes}
\usepackage{hyperref}
\usepackage[numbers, square]{natbib}
\usepackage{fancybox}
\usepackage{epsfig}
\usepackage{soul}
\usepackage[framemethod=tikz]{mdframed}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% _____ _ _ _____ _______ ____ __ __
% / ____| | | |/ ____|__ __/ __ \| \/ |
% | | | | | | (___ | | | | | | \ / |
% | | | | | |\___ \ | | | | | | |\/| |
% | |____| |__| |____) | | | | |__| | | | |
% \_____|\____/|_____/ |_| \____/|_| |_|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% _____ ____ __ __ __ __ _ _ _____ _____
% / ____/ __ \| \/ | \/ | /\ | \ | | __ \ / ____|
%| | | | | | \ / | \ / | / \ | \| | | | | (___
%| | | | | | |\/| | |\/| | / /\ \ | . ` | | | |\___ \
%| |___| |__| | | | | | | |/ ____ \| |\ | |__| |____) |
% \_____\____/|_| |_|_| |_/_/ \_\_| \_|_____/|_____/
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% SYNTAX FOR NEW COMMANDS:
%\newcommand{\new}{Old command or text}
% EXAMPLE:
\newcommand{\blah}{blah blah blah \dots}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% _______ ______ _____ _ _ ______ _____
% |__ __| ____| /\ / ____| | | | ____| __ \
% | | | |__ / \ | | | |__| | |__ | |__) |
% | | | __| / /\ \| | | __ | __| | _ /
% | | | |____ / ____ \ |____| | | | |____| | \ \
% |_| |______/_/ \_\_____|_| |_|______|_| \_\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% COMMANDS
% \clarity{points}{comment}
% \other{points}{comment}
% \spelling{comment}
% \units{comment}
% \english{comment}
% \source{comment}
% \concept{comment}
% \missing{comment}
% \maths{comment}
% \terms{comment}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\setlength{\marginparwidth}{3.4cm}
% NEW COUNTERS
\newcounter{points}
\setcounter{points}{100}
\newcounter{spelling}
\newcounter{english}
\newcounter{units}
\newcounter{other}
\newcounter{source}
\newcounter{concept}
\newcounter{missing}
\newcounter{math}
\newcounter{terms}
\newcounter{clarity}
% COMMANDS
\definecolor{myblue}{rgb}{0.668, 0.805, 0.929}
\newcommand{\hlb}[2][myblue]{ {\sethlcolor{#1} \hl{#2}} }
\newcommand{\clarity}[2]{\todo[color=CornflowerBlue!50]{CLARITY of WRITING(#1) #2}\addtocounter{points}{#1}
\addtocounter{clarity}{#1}}
\newcommand{\other}[2]{\todo{OTHER(#1) #2} \addtocounter{points}{#1} \addtocounter{other}{#1}}
\newcommand{\spelling}{\todo[color=CornflowerBlue!50]{SPELLING (-1)} \addtocounter{points}{-1}
\addtocounter{spelling}{-1}}
\newcommand{\units}{\todo{UNITS (-1)} \addtocounter{points}{-1}
\addtocounter{units}{-1}}
\newcommand{\english}{\todo[color=CornflowerBlue!50]{SYNTAX and GRAMMAR (-1)} \addtocounter{points}{-1}
\addtocounter{english}{-1}}
\newcommand{\source}{\todo{SOURCE(S) (-2)} \addtocounter{points}{-2}
\addtocounter{source}{-2}}
\newcommand{\concept}{\todo{CONCEPT (-2)} \addtocounter{points}{-2}
\addtocounter{concept}{-2}}
\newcommand{\missing}[2]{\todo{MISSING CONTENT (#1) #2} \addtocounter{points}{#1}
\addtocounter{missing}{#1}}
\newcommand{\maths}{\todo{MATH (-1)} \addtocounter{points}{-1}
\addtocounter{math}{-1}}
\newcommand{\terms}{\todo[color=CornflowerBlue!50]{SCIENCE TERMS (-1)} \addtocounter{points}{-1}
\addtocounter{terms}{-1}}
\newcommand{\summary}[1]{
\begin{mdframed}[nobreak=true]
\begin{minipage}{\textwidth}
\vspace{0.5cm}
\begin{center}
\Large{Grade Summary} \hrule
\end{center} \vspace{0.5cm}
General Comments: #1
\vspace{0.5cm}
Possible Points \dotfill 100 \\
Points Lost (Science Terms) \dotfill \theterms \\
Points Lost (Syntax and Grammar) \dotfill \theenglish \\
Points Lost (Spelling) \dotfill \thespelling \\
Points Lost (Units) \dotfill \theunits \\
Points Lost (Math) \dotfill \themath \\
Points Lost (Sources) \dotfill \thesource \\
Points Lost (Concept) \dotfill \theconcept \\
Points Lost (Missing Content) \dotfill \themissing \\
Points Lost (Clarity of Writing) \dotfill \theclarity \\
Other \dotfill \theother \\[0.5cm]
\begin{center}
\large{\textbf{Grade:} \fbox{\thepoints}}
\end{center}
\end{minipage}
\end{mdframed}}
%#########################################################
%To use symbols for footnotes
\renewcommand*{\thefootnote}{\fnsymbol{footnote}}
%To change footnotes back to numbers uncomment the following line
%\renewcommand*{\thefootnote}{\arabic{footnote}}
% Enable this command to adjust line spacing for inline math equations.
% \everymath{\displaystyle}
% _______ _____ _______ _ ______
%|__ __|_ _|__ __| | | ____|
% | | | | | | | | | |__
% | | | | | | | | | __|
% | | _| |_ | | | |____| |____
% |_| |_____| |_| |______|______|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\title{
\normalfont \normalsize
\textsc{The Hudson School, Hoboken, New Jersey \\
\hl{Physics, Winter Semester, 2016}}\\
[10pt]
\rule{\linewidth}{0.5pt} \\[6pt]
\huge Pendulum Lab \\
\rule{\linewidth}{2pt} \\[10pt]
}
\author{Carina Page}
\date{}
\begin{document}
\maketitle
\noindent
Date Performed \dotfill February 3, 2016 \\
Partners \dotfill Valerie Dowret \\
Instructor \dotfill Ari Raisa \\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% ______ ____
% | ____/\ / __ \
% | |__ / \ | | | |
% | __/ /\ \| | | |
% | | / ____ \ |__| |
% |_|/_/ \_\___\_\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Ctrl + / to comment out a group of lines.
%
%
% LIST MORE COMMON COMMMANDS
% LIST USEFUL WEBSITES FOR TABLES, ETC
% WHAT TO DO WHEN YOUR CODE WONT COMPILE
% OVERLEAF SHORTCUTS
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% _ ____
%| | /\ | _ \
%| | / \ | |_) |
%| | / /\ \ | _ <
%| |____ / ____ \| |_) |
%|______/_/ \_\____/
%%%%%%%%%%%%%%%%%%%%%%%%
% _____ _______ _____ _______ _____
% / ____|__ __|/\ | __ \__ __/ ____|
%| (___ | | / \ | |__) | | | | (___
% \___ \ | | / /\ \ | _ / | | \___ \
% ____) | | |/ ____ \| | \ \ | | ____) |
%|_____/ |_/_/ \_\_| \_\ |_| |_____/
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% _ _ ______ _____ ______
%| | | | ____| __ \| ____|
%| |__| | |__ | |__) | |__
%| __ | __| | _ /| __|
%| | | | |____| | \ \| |____
%|_| |_|______|_| \_\______|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Purpose}
The purpose of this experiment is to find which of the following three variables affect the period of the pendulum: length, mass, and/or amplitude.
% Yada Yada Yada
%#############################
% _ ___ _______ ____
%| | | \ \ / / __ \ / __ \
%| |__| |\ \_/ /| |__) | | | |______
%| __ | \ / | ___/| | | |______|
%| | | | | | | | | |__| |
%|_| |_| |_| |_| \____/
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% _______ _ _ ______ _____ _____ _____
%|__ __| | | | ____|/ ____|_ _|/ ____|
% | | | |__| | |__ | (___ | | | (___
% | | | __ | __| \___ \ | | \___ \
% | | | | | | |____ ____) |_| |_ ____) |
% |_| |_| |_|______|_____/|_____|_____/
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Hypothesis}
I think that the period of a pendulum depends on only the length of the pendulum because the pendulum with the longer string has a lower frequency and the shorter string has a shorter frequency.
%\cite{reference_number} in order to cite a source
%##########################################
% __ __ _______ ______ _____ _____ _ _____
%| \/ | /\|__ __| ____| __ \|_ _| /\ | | / ____|
%| \ / | / \ | | | |__ | |__) | | | / \ | | | (___
%| |\/| | / /\ \ | | | __| | _ / | | / /\ \ | | \___ \
%| | | |/ ____ \| | | |____| | \ \ _| |_ / ____ \| |____ ____) |
%|_| |_/_/ \_\_| |______|_| \_\_____/_/ \_\______|_____/
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section {Materials}
% Materials go here
\begin{enumerate}
\item C-clamp
\item \hl Ring-Stand
\item String
\item Pendulum with various masses
\end{enumerate}
%%%%%%%%%%%%%%%%%%%%%%%
% FOR A NUMBERED LIST
% \begin{enumerate}
% \item Your_Item
% \end{enumerate}
%%%%%%%%%%%%%%%%%%%%%%%
% FOR A BULLETED LIST
% \begin{itemize}
% \item Your_Item
% \end{itemize}
%%%%%%%%%%%%%%%%%%%%%%%
%#################################################################
% _____ _____ ____ _____ ______ _____ _ _ _____ ______
%| __ \| __ \ / __ \ / ____| ____| __ \| | | | __ \| ____|
%| |__) | |__) | | | | | | |__ | | | | | | | |__) | |__
%| ___/| _ /| | | | | | __| | | | | | | | _ /| __|
%| | | | \ \| |__| | |____| |____| |__| | |__| | | \ \| |____
%|_| |_| \_\\____/ \_____|______|_____/ \____/|_| \_\______|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section {Procedure}
\begin{enumerate}
\item Set up the ring stand
\item Apply vise grip to stand and table
\item Tie string to the pendulum clamp on the ring stand
\item \hl{attach} Attach a desired weight to the pendulum
\item Hold back pendulum to desired position
\item Release pendulum and track for 50 swings back and forth
\item Divide total time by 50 to get time for one period
\item Do this five times, but each time change length of the pendulum while keeping amplitude and mass the same. Then vary the amplitude while keeping mass and length the same. Lastly, vary mass while keeping the length and amplitude constant.
\end{enumerate}
%%%%%%%%%%%%%%%%%%%%%%%
% FOR A NUMBERED LIST
% \begin{enumerate}
% \item Your_Item
% \end{enumerate}
%%%%%%%%%%%%%%%%%%%%%%%
%##################################################################
% _____ _______
%| __ \ /\|__ __|/\
%| | | | / \ | | / \
%| | | |/ /\ \ | | / /\ \
%| |__| / ____ \| |/ ____ \
%|_____/_/ \_\_/_/ \_\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section {Data}
\includegraphics[width=\textwidth]{PendulumData.JPG}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% TO IMPORT AN IMAGE
% UPLOAD IT FIRST (HIT THE PROJECT BUTTON TO SHOW FILES)
% KEEP THE NAME SHORT WITH NO SPACES!
% TYPE THE FOLLOWING WITH THE NAME OF YOUR FILE
% DON'T INCLUDE THE FILE EXTENSION
% \includegraphics[width=\textwidth]{name_of_file}
% \textwidth makes the picture the width of the paragraphs
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% TO CREATE A FIGURE WITH A NUMBER AND CAPTION
% \begin{figure}
% \includegraphics[width=\textwidth]{image}
% \caption{Your Caption Goes Here}
% \label{your_label}
% \end{figure}
% REFER TO YOUR FIGURE LATER WITH
% \ref{your_label}
% LABELS NEED TO BE ONE WORD
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
We noticed that the release point had more of an effect on the time the pendulum took to do 50 rotations and not the mass.
As we released the pendulum we noticed that though we changed the release point, the time wasn't changing with it
%#############################
% _____ _____ _____ _____ _ _ _____ _____
%| __ \_ _|/ ____|/ ____| | | |/ ____/ ____|
%| | | || | | (___ | | | | | | (___| (___
%| | | || | \___ \| | | | | |\___ \\___ \
%| |__| || |_ ____) | |____| |__| |____) |___) |
%|_____/_____|_____/ \_____|\____/|_____/_____/
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section {Discussion}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
The most influential part was the length of the string.
\subsection{Results}
% State your main discovery based on the experimental data.
We discovered that mass doesn't matter as much as length does.The longer the string was the longer the period was and the shorter string had a shorter period
\subsection{Critique}
% Discuss precision of measurements and instruments.
% Suggest improvements for future labs.
Some of the measurements inaccuracies could of came from human error such as being unable to time the exact time of 50 rotations. Also, it could have came from the inability to let go of the pendulum at the same exact spot.
\subsection{Definitions}
\begin{enumerate}
\item Period (of a pendulum)- The time for one complete cycle, a left swing and a right swing, is called the period. The period depends on the length of the pendulum, and also to a slight degree on the amplitude, the width of the pendulum's swing.
\item Amplitude- the maximum extent of a vibration or oscillation, measured from the position of equilibrium.
\item Equilibrium- a state in which a process and its reverse are occurring at equal rates so that no overall change is taking place.
\item Linearizing equations- Linearizing equations is this process of modifying an equation to produce
new variables which can be plotted to produce a straight line graph. In
many of your labs, this has been done already
\item Simple Pendulum- Period of Simple Pendulum. A point mass hanging on a massless string is an idealized example of a simple pendulum. When displaced from its equilibrium point, the restoring force which brings it back to the center is given by: Show.
\item Physical pendulum- A physical pendulum is the generalized case of the simple pendulum. It consists of any rigid body that oscillates about a pivot point.
\end{enumerate}
%###############################################
% _____ ____ _ _ _____ _ _ _ _____ ______
% / ____/ __ \| \ | |/ ____| | | | | | __ \| ____|
%| | | | | | \| | | | | | | | | | | | |__
%| | | | | | . ` | | | | | | | | | | | __|
%| |___| |__| | |\ | |____| |___| |__| | |__| | |____
% \_____\____/|_| \_|\_____|______\____/|_____/|______|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Conclusion}
%#######################################################
In conclusion, this lab was very informative and showed the difference between the products of length, mass, and amplitude and how it affected a pendulum.
% _____ ____ _ _ _____ _____ ______ _____
% / ____|/ __ \| | | | __ \ / ____| ____|/ ____|
%| (___ | | | | | | | |__) | | | |__ | (___
% \___ \| | | | | | | _ /| | | __| \___ \
% ____) | |__| | |__| | | \ \| |____| |____ ____) |
%|_____/ \____/ \____/|_| \_\\_____|______|_____/
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% USE NOCITE TO ADD SOURCES TO THE BIBLIOGRAPHY WITHOUT SPECIFICALLY CITING THEM IN THE DOCUMENT
%\nocite{ref_num}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% BIBLIOGRAPHY: %
% Make sure your class *.bib file is uploaded to this project by clicking the project button > add files. Change 'sample' below to the name of your file without the .bib extension.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\bibliographystyle{plainnat}
%\bibliography{sample}
% UNCOMMENT THE TWO LINES ABOVE TO ENABLE BIBLIOGRAPHY
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\end{document} % NOTHING AFTER THIS LINE IS PART OF THE DOCUMENT
______ ______ ______ ______ ______ ______ ______
|______|______|______|______|______|______|______|
_____ ____
/ ____|/ __ \
| | __ | | |
| | |_ | | | |
| |__| | |__| |
\_____|\____/
_ _ ____ _____ _ _ ______ _______ _____ _
| | | |/ __ \| __ \| \ | | ____|__ __/ ____| |
| |__| | | | | |__) | \| | |__ | | | (___ | |
| __ | | | | _ /| . ` | __| | | \___ \| |
| | | | |__| | | \ \| |\ | |____ | | ____) |_|
|_| |_|\____/|_| \_\_| \_|______| |_| |_____/(_)
______ ______ ______ ______ ______ ______ ______
|______|______|______|______|______|______|______|