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# A#14 - y t of this system when the input is 2 sin t t x =...

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Assignment #14 ECSE-2410 Signals & Systems - Fall 2006 Tue 10/31/06 1(30). For the circuits shown, (A) (B). (a). Find ) ( s H (b). Sketch the general Bode straight-line magnitude diagram and indicate the general location of the break frequencies in terms of the circuit elements. (c). Sketch the Bode phase diagram. State whether the phase shift is leading (positive) or lagging (negative). 3(15). For the circuit shown, (a). Find ) ( s H . (b). Find the step response, ) ( t y step . (c). Use the MATLAB instruction, 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 ) ( 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,
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Unformatted text preview: y ( t ), of this system when the input is ) 2 sin( ) ( t t x = . 3(35 pts). Find the inverse Laplace transforms of the following, (a). 3 2 1 ) ( 2 + s + s = s X (b) 3 + 2s + s s = s X 2 ) ( . Solve using the cosine transform. (c). 3 + 2s + s s = s X 2 ) ( . Solve using the result in (a) and the property, ) ( ) ( s sX dt t dx = . Show that you get the same result as in (b). (d) ) 3 2 ( 1 ) ( 2 + s + s s = s X . (e) 1) + s + s ( 2) + (s 3 + s = s X 2 ) ( . Express answer in the form, ) ( cos t u Be u(t) ) + t ( e A t t-β α θ ϖ-+ . (f) 3 + 2s + s 0.5 + s = s X 2 ) ( . Express your answer in the form u(t) ) + t ( e C t-φ γ sin . (g) ( 29 ( 29 2 2 2 1 1 ) ( + + + =-s s e s X s...
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