me375_fa10_hwk04

me375_fa10_hwk04 - b) From your FBDs in a), derive the...

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ME 375 – Fall 2010 Homework No. 4 Due: Friday, September 24 Problem No. 1 (40%) The transfer function G s ( ) for a system with input U s ( ) and output Y s ( ) has the following properties: a static gain of 6 one zero: z 1 = -1 two poles: p 1 = ! 2 and p 2 = ! 4 For this system, a) determine the transfer function G s ( ) . b) determine the input/output differential equation for the system. c) determine the forced response y forced t ( ) for an input of u t ( ) = h t ( ) = unit step function . d) determine the forced response y forced t ( ) for an input of u t ( ) = r t ( ) = unit ramp function . t h(t) t = 0 1 t r(t) 1 1 t = 0
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Problem No. 2 (40%) The system shown above is made up of two blocks A and B (each of mass m), three springs (each of stiffness k), a dashpot (of damping coefficient c) and a moveable base C. Base C is given a PRESCRIBED motion of x C t ( ) ( x C t ( ) is the input for the system). Consider node D that connects the spring and dashpot to be massless. All springs are unstretched when x 1 = x 2 = x 3 = x C = 0 . a) Draw free body diagrams (FBDs) of A, B and D.
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Unformatted text preview: b) From your FBDs in a), derive the three differential equations of motion for the system. c) Determine the transfer function G 3 s ( ) = X 3 s ( ) / X C s ( ) for an input of x C t ( ) and an output of x 3 t ( ) . d) Determine the input/output differential equation of motion for x 3 t ( ) . e) What is the order of this system? x 1 smooth k C m smooth B A x 2 x 3 x C t ( ) c k k m D Problem No. 3 (30%) For the systems a) - f) below with output y t ( ) and input u t ( ) : develop the transfer function G s ( ) = Y s ( ) / U s ( ) . determine the poles of the transfer function. Locate (sketch) these poles in the complex plane. classify the systems as either: stable , unstable or marginally stable . a) !! y + 6 ! y + 25 y = 5 ! u t ( ) b) !! y ! 6 ! y + 25 y = 5 ! u t ( ) + 10 u t ( ) c) !! y + 6 ! y ! 25 y = ! 5 ! u t ( ) + 10 u t ( ) d) !! y ! 6 ! y ! 25 y = 10 u t ( ) e) !! y + 25 y = 3 u t ( ) f) !! y + 6 ! y = 3 u t ( )...
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me375_fa10_hwk04 - b) From your FBDs in a), derive the...

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