# HW4_Assg - V c ﬁnd the “mass-normalized” eigenvectors...

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Mechanical Vibrations Homework #4 Due: 18Oct04 - Start of Class Part 1: Work the following problem from the course text Prob: 7.11 Part 2: Work the following problems 1. Derive the equations of motion for the system shown in Figure 1. Use the following parameters: m = 3 Kg, I G = 4 Kg meters 2 , k 1 = k 2 = 200 N/meter, r = 2 meters. k 1 x(t) m k 2 I G r Figure 1: A two degree of freedom system with translation and rotation. 2. Find the eigenvalues and eigenvectors by hand and check your results with Matlab (or equivalent) for this problem. You are asked to: a) find the eigenvalues and natural frequencies for the system shown in Figure 1; b) find eigenvectors for each eigenvalue (

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Unformatted text preview: V ); c) ﬁnd the “mass-normalized” eigenvectors ( U ); and d) ﬁnd U T MU and U T KU if the resulting equation of motion was in the form. M ¨ ~ X + K ~ X = ~ (1) Example Matlab Matrix Operations : You can check your work, but make sure to turn in your hand calculations , using the following Matlab commands: 1 ﬁrst deﬁne the A-matrix: type A=[1 2; 3 4] a) transpose of the matrix A T , type A’ b) inverse of the matrix A-1 , type inv(A) c) calculate the eigenvalues and eigenvectors, type [vector,lamda]=eig(A) d) type “help eig” to learn more 2...
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