EML 5060 Analysis in Mechanical Engineering 11/3/97
Closed book Van Dommelen 10:45-11:35am

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 equation describing the field lines of an electrostatic field is

$$\frac{dx}{dy} = \frac{x^2-y^2}{2xy}.$$

Draw and describe the field lines. Solution.

2.

An electrical circuit involving two capacitors and two inductors is governed by the equation:

$$4 \stackrel{....}u + 8 \stackrel{..}u + 3 u = 0.$$

Find the general solution. Solution.

3.

The current in an RCL circuit with a certain applied voltage satisfies the equation:

$$2 \ddot u + 2 \dot u + u = \frac{e^{-\frac12t}}{\cos(\frac12t)}.$$

Find the current, assuming that $u(0)=\dot u(0) = 0$.Solution.