%Linear Second-order ODE's %If you modify this file, please indicate here and in the footnote %Math340 \documentclass[12pt]{article} \usepackage{times} \pagestyle{empty} \addtolength{\textwidth}{1.2in} \addtolength{\textheight}{1.2in} \addtolength{\oddsidemargin}{-.58in} \addtolength{\evensidemargin}{-.58in} \renewcommand{\baselinestretch}{1.0} \parindent = 0cm \parskip = .1cm \begin{document} \begin{center} {\Large Linear Second-order Equations \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 Enter the following commands: \begin{enumerate} \item \verb&y = dsolve('D2y+y=0', 'y(0)=1', 'Dy(0)=1')& \item \verb&ezplot(y, [0, 100]) & \item Explain exactly what happened. \end{enumerate} \vspace{.2cm} \item Repeat the above procedure to solve and plot the solutions for the following differential equations. Use the same initial condition as above. \begin{enumerate} \item $y''(t) + y(t) = \sin(t)$ \item $y''(t) + 0.1 y' + y(t) = 0$ \item $y''(t) + 0.1 y' + y(t) = \sin(t)$ \end{enumerate} \item Compare the differential equations in the four examples. Then compare the graphs of the solutions in the examples. Based on things you have learned in class, explain the differences between the examples. \item Prepare a brief (\verb$< $1 page) written report answering all the questions and sketching the graphs carefully by hand. Use complete sentences and standard mathematical notation. Do {\bf not} get a printout. \end{enumerate} \vfill \noindent \textsf{ Students explore the interaction of damping, restoring, and forcing effects on the solution.} \end{document}