Homework 10 1. Problem 7.6 in the textbook. The second sentence of the problem should say, “Assume that mass undergoes small angular displacements…” Ignore weight in this problem. You will need to express rotation and the mass center displacement of in terms of and . You should get EOMs in the form . Are the matrices symmetric? Next derive EOMs by using Lagrange’s equations. Derive carefully by imagining the virtual work done by the dashpot forces through all four virtual displacements. Before using Lagrange’s equations, make sure that the kinetic energy is expressed in terms of and rather than and . Now are the matrices symmetric? Do these EOMs “agree” with the ones you derived using the Newtonian approach? If so, how? 2. Problem 7.1 in the textbook. Deriving these equations of motion using Newton’s second law is very similar to what was done in the lecture notes. Next, obtain as in the lecture, check that as in the lecture, and use Lagrange’s equations to derive EOMs. Work problems 7.19, 20, 37 and 38, using MATLAB. (For vibration about
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