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Unformatted text preview: ME 563 HOMEWORK # 4 SOLUTIONS Fall 2008 Out: September 29, 2008 Due: October 6, 2008 (at 5 p.m. EST) Problem 1 FBD Summation of forces on the element: Response is of the form: Solve second order differential equations with boundary conditions: dx Problem 2 FBD Assumptions Constant tension and density Small deflections EOM: Response is of the form: Hence: Boundary conditions: M T (L) Negative slope, Solving differential equation for spatial component and applying the two boundary conditions: Since: We get: Problem 3 Using 10 lumped masses in Problem 1, we have density and area as constants. Hence, the EOMs for free free boundary conditions are as follows: 1 10 1 10 10 2 1 10 10 1 10 10 2 1 10 10 10 10 10 20 10 10 10 10 10 10 x x x x x u u u L AE L AE L AE L AE L AE L AE L AE u u u AL AL AL =...
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 Fall '09
 Boundary conditions

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