HW4 - ME 375 HOMEWORK 4 Spring 2009 Out February 4 2009...

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ME 375 HOMEWORK # 4 Spring 2009 Out: February 4, 2009 Due: February 11, 2009 (at the beginning of class) PROBLEM 1: (40%) Consider the following set of differential equations that represent an engine supported by elastomeric mounts and excited by a reciprocating force, f ( t ) (see Figure 1): = + + 0 ) ( 5 . 0 5 . 0 5 . 0 5 . 1 1 . 0 0 0 0 0 0 0 1 t f y x y x y x ± ± ± ± ± ± These equations describe an engine, which is isolated from its chassis by a mount that possesses frequency dependent damping and stiffness. Answer the following questions. Figure 1 (a) Solve for the Laplace transforms, X ( s ) and Y ( s ), of x ( t ) and y ( t ), respectively, in terms of the Laplace transform, F ( s ), of f ( t ) and the initial conditions of the system. (b) For f ( t ) = 0 N with initial conditions y (0) = 0 m, x (0) = 0 m, and 1 . 0 ) 0 ( = x ± m/s, solve for x ( t ).
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