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Unformatted text preview: Homework 6.1
For this problem:
1. Derive the mass and stiﬀness matrices for the system in terms of the absolute generalized
coordinates x1 and x2 . Assume the disk to be homogeneous.
2. Determine the natural frequencies for the system. Leave your natural frequencies in terms of
k /m and α.
3. Determine the beat period for the free response of the system corresponding to α << 1. Homework 6.2
For this problem:
1. Derive the mass, damping and stiﬀness matrices for the system in terms of the absolute generalized coordinates x1 and x2 .
2. Show that the system possesses Rayleigh damping. Does the system possess either mass proportional (external) or stiﬀness proportional (internal) damping?
3. Determine the undamped natural frequencies in terms of k /m. 4. Write down the uncoupled EOMs in terms of modal coordinates p1 (√ and p2 (t). Determine
t)
the modal damping ratios for the two modes of the problem. Use c/ km = 0.3. Homework 6.3
Consider the longitudinal motion u(x, t) of the thin rod shown below. Determine the natural frequencies and modal functions for this rod. ...
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This document was uploaded on 12/23/2011.
 Fall '09

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