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{\bf EML 5060 \hfill Analysis in Mechanical Engineering \hfill 11/3/97}\\
{\it Closed book \hfill Van Dommelen \hfill 10:45-11:35am}
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Show all reasoning and intermediate results leading to your answer.
One book of mathematical tables, such as Schaum's Mathematical Handbook,
may be used.

\begin{enumerate}

\item
The equation describing the field lines of an electrostatic
field is
\begin{displaymath}
    \frac{dx}{dy} = \frac{x^2-y^2}{2xy}.
\end{displaymath}
Draw and describe the field lines.
\begin{rawhtml}
<A HREF="figures/1.gif">Solution.</A>
\end{rawhtml}

\item
An electrical circuit involving two capacitors and two inductors
is governed by the equation:
\begin{displaymath}
   4 \stackrel{....}u + 8 \stackrel{..}u + 3 u = 0.
\end{displaymath}
Find the general solution.
\begin{rawhtml}
<A HREF="figures/2.gif">Solution.</A>
\end{rawhtml}

\item
The current in an RCL circuit with a certain applied voltage satisfies
the equation:
\begin{displaymath}
    2 \ddot u + 2 \dot u + u = \frac{e^{-\frac12t}}{\cos(\frac12t)}.
\end{displaymath}
Find the current, assuming that $u(0)=\dot u(0) = 0$.
\begin{rawhtml}
<A HREF="figures/3.gif">Solution.</A>
\end{rawhtml}

\end{enumerate}

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