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Decsribe underdamped free vibrations. Show calculations and all necessary diagrams.

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Consider the sheet formed by the intersection of the curves: x = 0, x = 4, y = 0, y = 3 [=] cm, with a variable density of mass per unit area ρ(x,y) = xy [=] g/cm2 . Write and evaluate multiple integrals to calculate the following: a. The area of the sheet [=] cm2 . b. The mass of the sheet [=] g. c. The shell moments about the x & y axes (Mx & My) [=] g∙cm. d. The position of the center of mass of the sheet ( , ) [=] cm.