Homework 81.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(=-MKiλfor each of the eigenvalues found and that uuMKλ=for each eigenpair ),(uλ, and finally that KUUTand MUUTyield 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 3mundergoes small angular displacements…” Ignore weight in this problem. You will need to express rotation θand the mass center displacement Cxof 3min terms of 1xand 2x. You should get EOMs in the form 0xxx=++KCM. Are the matrices symmetric? Next derive EOMs by using Lagrange’s equations. Derive ncWδcarefully by imagining the virtual work done by the dashpot forces through all four virtual displacements.
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