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me375_fa10_hwk06

# me375_fa10_hwk06 - ME 375 Fall 2010 Homework No 6 Due...

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ME 375 – Fall 2010 Homework No. 6 Due: Friday, October 15 Problem No. 1 (40%) A system is made up of connector A (of negligible mass), movable support D, three springs and a dashpot, connected as shown in the figure above. Support D is given a PRESCRIBED displacement of y D t ( ) = du t ( ) , where u t ( ) is the input to the system. All springs are unstretched when y D = y = 0 . For this problem: a) Draw an appropriate free body diagram (FBD) of the massless connector A. From this FBD, derive the equation of motion (EOM) of the system with the displacement of block A, y , being the output. b) Based on your EOM from a), determine the transfer function G s ( ) = Y s ( ) / U s ( ) . c) For u t ( ) = sin ! t , we know that the steady-state response of the system can be written as: y ss t ( ) = G j ! ( ) sin ! t + " G j ! ( ) ( ) . Develop expressions for the amplitude G j ! ( ) and phase of the response ! G j " ( ) in terms of c , k and d . d) A time history of the steady-state response of this system for u t ( ) = sin 2 t is shown in the figure on the following page for k = 10 N / m . From this plot, estimate values of c and d for this system.

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