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# hwk03 - ME 375 HOMEWORK#3 Spring 2010 Out Jan 27th 2010 Due...

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ME 375 HOMEWORK #3 Spring 2010 Out: Jan. 27 th , 2010 Due: Feb. 3, 2010 PROBLEM 1 : (40%) A block of mass m is able to slide on a smooth, horizontal surface. The center of the block O is connected to ground with two pairs of spring-dashpot components, as shown in the figure. A horizontal force f(t) acts at O. Let x and y represent displacements of O and A, respectively, with the springs being unstretched when x = y = 0, and where A is a massless node connecting the two pairs of spring-dashpot components. a) Draw individual free body diagrams (FBDs) of the block and of node A. From these FBDs, derive the equations of motion (EOMs) for the system in terms of the coordinates x(t) and y(t). b) Suppose c 1 = c 2 = 0. Reformulate your EOMs in a) as a single input/output equation with f(t) as the input and x(t) as the output. Note that with c 1 = c 2 = 0, the two springs are connected in series. Is the stiffness term in your input-output equation consistent with having these two springs in series? What is the order of this system?

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hwk03 - ME 375 HOMEWORK#3 Spring 2010 Out Jan 27th 2010 Due...

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