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# ps09 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering 2.004 Dynamics and Control II Fall 2007 Problem Set #9 Posted: Friday, Nov. 16, ’07 Due: Wednesday, Nov. 28, ’07 1. In this problem, we will analyze the 2.004 Tower system (including the compen- sating mass–damper–compliance slider components) using the eigenvalues/eigenvectors of its state matrix. The system parameters are m 1 = 5 . 11kg, b 1 = 0 . 767N · sec / m, k 1 = 2024 N / m; m 2 = 0 . 87 kg, b 2 = 8 . 9 N · sec / m, k 2 = 185 N / m. The system model schematic is shown again below for your convenience. a) Substitute these values into the system matrix A that you derived in Prob- lem Set 8 (or use the solution to Problem Set 8 that has been posted online if you haven’t kept a copy of your solution) and use Matlab to compute the eigenvectors and eigenvalues as follows: [va,da]=eigs(a) . This will return two matrices va and da . The columns of matrix va are the eigenvectors; the diagonal elements of matrix da are the eigenvalues corresponding to the eigenvectors column–by–column.

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