228_w06_solve_DE_practice

228_w06_solve_DE_practice - EE 228: Continuous-Time Signals...

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Unformatted text preview: EE 228: Continuous-Time Signals and Systems Cal Poly, slo Practice problem Solving at 2‘“l order system using y(t) = yN(t) + yF(t) method and y(t) = yZI(t) + yzs(t) method John Saghri Find the response ofthe system described by the following differential equation; y”(t) + 4y’(t) + 3y(t) = 2X’(t) + x(t) with X(t) = 6u(t), y(0) = 7, y'(0) = -3 7 Method 1 [Using y(t)=yN(t) +yF(t) method] Skarli mil—la stage—input SyS-lem) - {mm gm Argyocfi) ; xoeq) -: and) cal “S'ii'hCé %'FCEW%.Fonc_Jfinn 7<(-k)=b( we. OsSOME SUbgl‘il—Jle (n JCO 0b+q'.n _+L¥S+3 =(S+3)(S+\)_=o fist-:4) gar—93 '33? SJC JC 2 9— Jc *BJC VNDC) kie +kze_ : k‘a JAR: "?;(JC)-‘=_)’FI.JUC)+yN'(JC) :_ 1 fig: high Ema-fig age. 861, 3 0 Vote 2 49-513- kzgfi do“ A Usé i'm'l‘i’al 'Q'dh‘lr; n. 5 I A. _ - ' ares-Feared; SEEQJMJ OM )’ (0)7"3 ‘Y‘E‘l‘?’ dab . l+kr¥kz :7 I g "2?; kxaéfl<2= —.\ 4t “kt—’3: leans-=- —-"5 fit git r _-t- ‘ "\ Z 'e A'- 61, 2;») ~—<75Q +3 62 , Sim‘Q Sys'lemis UV: 0 Yo 1 / / fit 4i ,2 6 “a £31. y(’c\=7_>/O(JU +\/DL+)=2.[—ée +%€. +‘ + 9- ' it at Answer: Wt) = 2- 6 e. _-\-‘5.€ Method 2 [Using y(t) = yZI(t) + yzs(t) method] CE a Sz+q5+3 :L$+\)(S+3):Q ~—_381:.H-—-[) 822—3. Finoh'vmd, ZTR (Assume. _$\‘Y\%\Q_.-EV\\PU\—) St E *1: ‘3 yew = m _ use {NJer conokt'fl'ons 7(03r7gl y/(o)=~3 ‘Eo objrmlv) k.+kL—.7 i‘k\ fakz: "-3 "3-": 3:2 r; \[Fkfl =2 wig-1.: . \ C€W?:an¢-W" ' u t Ms) VFW 51mm 2 2 4. no“? 51 M22 3 §;\‘v\ce_ Z4210 S’mffeh-fi 2 >l/(O): O ‘ I {id—kI-I— k2 =0 I Bé-‘Ea—th *k flak “ 7?}: kF—zgit) klzxtta {2}“:2} 'i 2. "“ _t __ 5 _ __3- ’ - —-3 w);- YZ (m yaw: q (—1 —2e3 1+ 1—3“: fig-“'6 egigt 3% mm’ry Wm? YJHP/owli‘éem “+45 ‘6 at at y(t)=1-6€+Se @ B , SUB$¥EJXU¥Q M DE ...
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This note was uploaded on 10/06/2010 for the course EE EE 228 taught by Professor Saghri during the Spring '10 term at Cal Poly.

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228_w06_solve_DE_practice - EE 228: Continuous-Time Signals...

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