ME 375 HOMEWORK #7 Fall 2010Out: October. 15th, 2010 Due: October 22th, 2010 PROBLEM 1: (30%) (a)The model of a certain mass-spring-damper system is 1020( )xcxxf t++=&&&How large must the damping constant cbe so that the maximum steady-state amplitude of xis no greater than 3, if the input is( )11sinf ttω=, for an arbitrary value of ω? (b)The dynamic equation of a second order system subject to a sinusoidal input can be written as 202( )sinnnxxxf tftζωωω++==&&&The figure below shows the scaled input 0( )/f tfand the steady state response ( )x t. Find the natural frequency nωand the damping ratio ζof the system. PROBLEM 2(30%) Sketch the Bode plots of the following transfer functions using asymptotes. Show your work clearly. After completing the hand sketches, verify your results using MATLAB. Turn in your sketches and the MATLAB results on the same scales. (a) 100( )(0.11)(0.51)G ssss=++(b) 21( )310G sss=++(c) 2(5)( )(10)sG ss s+=+
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