MATH 2250 § 2 THIRD LAB ASSIGNMENT Nov. 8, 2002 A. Treibergs Due Nov. 27, 2002

• This lab deals with the analysis of a model of a seven story building being shaken by an earthquake. Each floor of the building is assumed to be connected to the adjacent floors by springy material, and so the equations for the displacements of individual floors resemble those for the masses of a coupled spring/mass system. The building is subjected to an oscillatory force from an earthquake. How do different frequencies of shaking affect the building? Read the description of the third lab assignment, which is Computing Project 7.4. You will need to review the sections on forced oscillations and resonance from section 7.4. The first part of the lab deals with setting up the model and finding the eigenvalues of the unforced system, which give you the natural frequencies for building wobble. The second part asks you to find the steady state response for shaking of a given frequency. You will discover that the building is sensitive to shaking at several very specific frequencies.

• Do all parts of problems 3.1-3.6. Remember, that this is a lab writeup whose purpose is to show how the computer plays a role in solving problems. It is not just an exercise in running somebody's code. Please make your writeups SELF-CONTAINED. This simply means that for each problem you would include a sentence or two stating what the problem is about and your conclusions. For example, include a short description of the model. You may wish to comment on its shortcomings after your analysis. And include some explanation of how the solution of the linear system in problem 3.3-3.6 relates to the steaqdy state solution for the building shake. You can use the templates, but they have to be suitably enhanced. It is perfectly OK to write by hand on your output. Or use MAPLE's capability of inserting comment text.

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