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ASE 365 - HW 8 - Homework 8 1 Problem 7.2 in the textbook...

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Homework 8 1. Problem 7.2 in the textbook. Derive equations of motion first by using Newton’s second law, and then by using Lagrange’s equations. (They should agree!) Then do problem 7.21 in the textbook. You can use the “eig” command in MATLAB, but check that 0 ) det( = - M K i λ for each of the eigenvalues found and that u u M K λ = for each eigenpair ) , ( u λ , and finally that KU U T and MU U T yield diagonal matrices. Plot modes as in Fig. 7.5. Finally, “mass-normalize” them so that they satisfy Eqs. (7.92). 2. Problem 7.6 in the textbook. The second sentence of the problem should say, “Assume that mass 3 m undergoes small angular displacements…” Ignore weight in this problem. You will need to express rotation θ and the mass center displacement C x of 3 m in terms of 1 x and 2 x . You should get EOMs in the form 0 x x x = + + K C M . Are the matrices symmetric? Next derive EOMs by using Lagrange’s equations. Derive nc W δ carefully by imagining the virtual work done by the dashpot forces through all four virtual displacements.
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