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me375_fa10_hwk06_soln

# me375_fa10_hwk06_soln - u t = sin t we know that the...

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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

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Unformatted text preview: 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. HINT : Consider the amplitude and phase of the steady-state response in the steady-state time history plot shown. 3 c massless connector y 2 k c y D t ( ) k D A movable support...
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me375_fa10_hwk06_soln - u t = sin t we know that the...

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