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{\bf EML 5060 \hfill Analysis in Mechanical Engineering \hfill 9/22/95 }\\
{\it Closed book \hfill Van Dommelen \hfill 9:00-9:50 EST}
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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.

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\item
The velocity components in front of a body with a hole are:
$$u=2 y - {2y\over x^2+y^2} \qquad v = 2x + {2x\over x^2+y^2}.$$
The `streamlines' of a flow can be found from
$$ v \, {\rm d}x - u \, {\rm d}y = 0.$$
Find the equation of the streamlines in this flow.
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  <a href="figures/1.gif">Solution</a>
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\item
A damped spring mass system experiences an external force,
resulting in an equation of motion
$$ \ddot x + 4 \dot x +13 x = e^{-2t} + t +1.$$
Find the general motion of the mass $x(t)$.
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  <a href="figures/3.gif">Solution</a>
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\item
The equation governing a beam in a destabilizing force field is:
$$y'''' - y = 0.$$
Find the shape of the beam $y(x)$ given the initial conditions
$$y(0)=y'(0)=y''(0)=0, \qquad y'''(0)=1.$$
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  <a href="figures/3.gif">Solution</a>
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