me375_sp11_hwk06

me375_sp11_hwk06 - ME 375 Spring 2011 Homework No. 6 Due:...

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ME 375 – Spring 2011 Homework No. 6 Due: Friday, March 4 th Problem No. 1 (40%) A piece of industrial equipment A (with mass m) is connected to ground with a pair of parallel spring and dashpot components (having stiffness k and damping coefficient c, respectively) as shown above. A force of 0 () f tf u t = is applied to the equipment. As seen earlier in the course, the transfer function between the input ut and the response y t is given by 00 22 2 / 2 nn ff m Ys Us m s c s k s s ζ ωω == ++ + + Where / n km ω = and /(2 ) ck m = . The force transmitted to the wall by the spring and dashpot can be written as: T f cy ky = + ± and the transfer function between the transmitted force T f and the response y becomes: 2 (2 ) T Fs cs k m s =+= + It is desired to choose a spring stiffness to make the amplitude of the steady-state transmitted force ( ) T f t to be as small as possible for an input of () s in t = . (a) Determine the transfer function ( ) ( ) / ( ) T Gs F s Us = relating the transmitted force T f t for an input . Write your result in terms , 0 f , and / n s .
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me375_sp11_hwk06 - ME 375 Spring 2011 Homework No. 6 Due:...

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