me375_fa10_hwk05

me375_fa10_hwk05 - ME 375 Fall 2010 Homework No. 5 Due:...

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ME 375 – Fall 2010 Homework No. 5 Due: Friday, October 1 Problem No. 1 (40%) A force f t ( ) = f 0 u t ( ) is applied to block A of the two-DOF system shown above. Assume all surfaces to be smooth and that the springs are unstretched when x 1 = x 2 = 0 . For this system: a) Derive the EOMs in terms of the coordinates x 1 and x 2 . b) Develop the transfer function G s ( ) = X 2 s ( ) / U s ( ) corresponding to an output of x 2 t ( ) and an input of u t ( ) . c) Determine the four poles p 1 , p 2 , p 3 , p 4 ( ) of the transfer function in b). Plot these poles in the complex plane. Use m = 1 kg and k = 100 N / meter . d) Based on the poles found in c) above, classify the stability of the system (unstable, stable or marginally stable). e) Suppose that we are interested in the forced response of x 2 t ( ) for an input of u t ( ) = ! t ( ) = unit impulse function . With this input, we know that the partial- fraction expansion of the response x 2 t ( ) can be written as: x 2 t ( ) = A 1 e p 1 t
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me375_fa10_hwk05 - ME 375 Fall 2010 Homework No. 5 Due:...

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