%Spring-mass system
%If you modify this file, please indicate here and in the footnote
%Math340
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\begin{document}
{\begin{center}
{\Large
A Spring-Mass System\footnote{Copyright \copyright 2002 Larry Snyder and Todd Young.
All rights reserved. Please address comments to young@math.ohiou.edu.}}
\end{center}
\begin{enumerate}
\item Type the following commands (at the prompt and then press
\fbox{Enter}): \vspace{-.2cm}
\begin{enumerate}
\item \verb&syms a&
\item \verb&y = dsolve('2*D2y+.5*Dy+5*y=sin(a*t)','y(0)=1','Dy(0)=1') &
\item \verb&y1 = subs(y, a, 1) & \dotfill Substitutes ``1'' for \verb$a$.
\item \verb&ezplot(y1, [0,50]) &
\item Explain exactly what happened.
\end{enumerate}
\vspace{.2cm}
\item Repeat (b) and (c) for different values of \verb&a&, both more and less than \verb$1$.
By trial and error find a value of \verb$a$ that maximizes the amplitude of the solution.
From the equation, what is its `natural' or `resonant' frequency?
What should happen when \verb&a& is set to this value?
Test your hypothesis.
\vspace{.2cm}
\item Prepare a brief (\verb$< $1 page) written report answering all
the questions. Use complete sentences and standard mathematical notation.
Do {\bf not} get a printout.
\end{enumerate}
\vfill
\noindent
{\sf The user examines what happens when a system is excited at different frequencies,
the relationship between natural frequency and amplitude of the forced, damped ocsillator.}
\end{document}
