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EML 5060 Analysis in Mechanical Engineering 9/22/95
Closed book Van Dommelen 9:00-9:50 EST
Show all reasoning and intermediate results leading to your answer.
One book of mathematical tables, such as Schaum's Mathematical Handbook,
may be used.
- 1.
- The velocity components in front of a body with a hole are:
![\begin{displaymath}
u=2 y - {2y\over x^2+y^2} \qquad v = 2x + {2x\over x^2+y^2}.\end{displaymath}](img1.gif)
The `streamlines' of a flow can be found from
![\begin{displaymath}
v \, {\rm d}x - u \, {\rm d}y = 0.\end{displaymath}](img2.gif)
Find the equation of the streamlines in this flow.
Solution
- 2.
- A damped spring mass system experiences an external force,
resulting in an equation of motion
![\begin{displaymath}
\ddot x + 4 \dot x +13 x = e^{-2t} + t +1.\end{displaymath}](img3.gif)
Find the general motion of the mass x(t).
Solution
- 3.
- 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
![\begin{displaymath}
y(0)=y'(0)=y''(0)=0, \qquad y'''(0)=1.\end{displaymath}](img4.gif)
Solution
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