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hwk05 - ME563 Fall 2011 Purdue University West Lafayette IN...

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ME563 – Fall 2011 Purdue University West Lafayette, IN Homework Set No. 5 Assignment date : Friday, September 23 Due date : Friday, September 30 Please attach this cover sheet to your completed homework assignment. Name PUID Problem 5.1 Problem 5.2 Problem 5.3 TOTAL
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ME 563 – Fall 2011 Homework Prob. 5.1 The system shown below is made up of a block A of mass 2m , a spring of stiffness k and a thin, homogeneous bar of mass m and length L . The spring is unstretched when x = 0 . a) Determine the mass and stiffness matrices of the system corresponding to the generalized coordinates x and θ for small motion about the equilibrium state of x 0 = θ 0 = 0 . b) Determine the natural frequencies and mode shapes for the system. Make sketches of the mode shapes. Do all your calculations by hand. Use kL / mg = 2 . c) Determine the response x t ( ) and θ t ( ) corresponding to initial conditions of x 0 ( ) = θ 0 ( ) = θ 0 ( ) = 0 and x 0 ( ) = v 0 . A m , L θ g smooth 2 m x k
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ME 563 – Fall 2011 Homework Prob. 5.2
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