me375_fa10_hwk07

me375_fa10_hwk07 - ME 375 HOMEWORK#7 Out October 15th 2010...

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ME 375 HOMEWORK #7 Fall 2010 Out: October. 15 th , 2010 Due: October 22 th , 2010 PROBLEM 1 : (30%) (a) The model of a certain mass-spring-damper system is 10 20 ( ) x cx x f t + + = && & How large must the damping constant c be so that the maximum steady-state amplitude of x is no greater than 3, if the input is ( ) 11sin f t t ω = , for an arbitrary value of ω ? (b) The dynamic equation of a second order system subject to a sinusoidal input can be written as 2 0 2 ( ) sin n n x x x f t f t ζω ω ω + + = = && & The figure below shows the scaled input 0 ( )/ f t f and the steady state response ( ) x t . Find the natural frequency n ω and the damping ratio ζ of 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 ( ) (0.1 1)(0.5 1) G s s s s = + + (b) 2 1 ( ) 3 10 G s s s = + + (c) 2( 5) ( ) ( 10) s G s s s + = +
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