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{\bf EML 5060 \hfill Analysis in Mechanical Engineering \hfill 11/5/01}\\
{\it Closed book \hfill Van Dommelen \hfill 10:35-11:25am}
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Show all reasoning and intermediate results leading to your answer, or
credit will be lost. One book of mathematical tables, such as Schaum's
Mathematical Handbook, may be used, as well as a calculator.
Work very carefully.

\begin{enumerate}
  
\item The equation governing streamlines in two-dimensional flows is
  \begin{displaymath}
    \frac{{\rm d}y}{{\rm d}x} = \frac vu
  \end{displaymath}
  For some flow, the velocity components are
  \begin{displaymath}
    u=2x^2y + 2 y \qquad v = - 2x y^2-2 x
  \end{displaymath}
  Find and neatly draw the streamlines of this flow.  (30 points for
  solving, 3 points for drawing.)

\begin{rawhtml}
<A HREF="figures/1.gif">Solution.</A>
\end{rawhtml}


\item Solve the following equation describing a damped spring mass
  system subject to a decaying external force:
  \begin{displaymath}
    \ddot x + 3 \dot x + 2 x = e^{-t} + e^{-2t} + e^{-3t}
  \end{displaymath}

\begin{rawhtml}
<A HREF="figures/2.gif">Solution.</A>
\end{rawhtml}

\item Solve the {\em homogeneous part} of the equation of question 2
  as a system of first order equations in the way it was done in
  class.

\begin{rawhtml}
<A HREF="figures/3.gif">Solution.</A>
\end{rawhtml}

\end{enumerate}

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