Assignment #19 ECSE-2410 Signals & Systems - Spring 2009 Due Tue 04/07/09 R =2 Ω L =2 H C = 8 1 F x(t) y(t) 1(20). Given the RLC circuit shown, (a)(5). Find , ) ( s H n ω ζ , , sketch pole-zero plot. (b)(5). Use MATLAB to plot the Bode magnitude and phase diagrams. (c)(5). Use Laplace transforms to compute the step response. Express your solution in the form, . ) ( ) cos( ) ( ) ( t u E Dt Be t Au t y t C + + = − (d)(5). Use MATLAB step(num,den) , to plot the step response. 2(20). A second-order system is described by the differential equation ) ( ) ( ) ( 2 ) ( 2 2 t x t y dt t dy dt t y d K = + + , where K is an unknown constant. (a)(5). Find using the derivative property of Laplace transforms. ) ( s H (b)(5) Find the value of K that will make the system critically damped. (c)(10) If K = 1, what is the output, y ( t ), of this system when the input is . ) 2 sin( ) ( t t x = 3(30). A Butterworth lowpass filter of order
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