EML 5060 Analysis in Mechanical Engineering 10/18/94
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. Jack Tsai may use one English or English-Chinese dictionary.

1.

An object cools from 100 degrees to 60 degrees in 10 minutes. If the rate at which it cools is proportional to the difference in temperature from the 20 degree ambient air temperature, what is the temperature after 40 minutes?

2.

The equation for a beam experiencing a load proportional to its deflection is:

y'''' -16 y = 0

Find the general form of the deflection y(x).

3.

A mass is moving through a fluid with a viscosity that varies linearly with position. After rescaling, the normalized equation of motion becomes

$$\ddot x + 2 x \dot x = 0$$

Find and sketch the position x(t), assuming that at time t=0 the position x=0 and velocity $\dot x=1$.