EML 5060 Analysis in Mechanical Engineering 11/8/99
Closed book Van Dommelen 10:45-11:35am

Show all reasoning and intermediate results leading to your answer, or credit will be lost. One book of mathematical tables, such as Schaum's Mathematical Handbook, may be used, as well as a calculator and a single A4-size handwritten formula sheet.

1.

The streamlines in a certain ideal flow satisfy

Find and draw the streamlines of this flow. Solution.

2.

In a certain dynamical system with two degrees of freedom, the equation of motion for one of the degrees of freedom u has been derived as

The initial conditions at time t=0 involve kinetic energy only: , .Find the degree of freedom u for any time. Also, what are the natural frequencies of the system? (Note: the last term should have been 4u.) Solution.

3.

The equation of motion of the simplest spring-mass system is, of course,

Solve this equation completely as a first order system according to the procedure explained in class. Show that this leads to the usual well-known solution for the motion of a spring-mass system. Solution.