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HW5 - ME 375 HOMEWORK#5 Spring 2009 Out Due(at the...

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ME 375 HOMEWORK #5 Spring 2009 Out: February 11, 2009 Due: February 18, 2009 (at the beginning of class) PROBLEM 1: (35%) Consider the following differential equation that represents 3 masses connected by dampers: 4 3 ( ) + + = ±±± ±± ± v v v f t where v is the velocity of the leftmost mass, and f ( t ) is the applied force acting on this mass. (a) Determine the transfer function relating V ( s ) to F ( s ). (b) Determine the transformed free response V ( s ) when ( ) 0, (0) 1, (0) 1, (0) 2 = = = − = ± ±± f t v v v , corresponding to a nonzero initial velocity for the leftmost mass and zero initial velocities for the other two masses. (c) Compare your expression for V ( s ) in part (b) with your transfer function in part (a). Do you see any similarities? (d) Expand your answer in part (b) using partial fraction expansion and solve for the free response v ( t ). (e) What part of the transfer function determines the form of the free response? PROBLEM 2 : (30%) For the system given by 4 ( ), (0) (0) 0 + + = = = ±± ± ± x bx x F t x x (a) Determine the transfer function that relates the transformed output X (
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