HW8_sol - Problem saf- g Eofufioné PTDHEM =2? 1 a.)...

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Unformatted text preview: Problem saf- g Eofufioné PTDHEM =2? 1 a.) SkS—l- la (51(5) HES): sl+£5k+1)s+lo 2 1+ QCSJFCSJ (5k3+ro}/CS?—+E) H JI+ EKS+EG 31-3-13 [19 1+QEEJF'CE) = 1+ 5K5+10 S£S+2) 90+, we new +H€ ~FoHom‘r-13 ¥D~rm '~ HumETQfiyr DE nominth There-Fave) Mulfipfy anal divide ® by {31+ 3—3 '1' '0) , (“15+ “53/ (51+23+ Io) 5K3 51+23+Io f+ @633I1Cs): 1+ R HCE) : 1+ mereJPom, Hag charqc+Er1'si-'EC ectuqfion EECGMESJ | '53 ~--Psn5 : K ———"F——-—-—' ! r+ QfiSJFiS) I+ 32+ 25 + to I 1.) 5kg GEE) FCS‘) : Sl+gg+ 10 THE Compiex PO‘E‘S are, if '1 i— gi , Sum (34': o—Hme qnjufqr Can’rffbuh‘ons rant tramway PC3195 is. BQO . T'Re zero [5 q+ =5ch qnd hem-e 4-H: enHre. nesafive x-axis (fife fecal axis) is qui- a? Have: we? Mums. r ' Problem #2‘ ’1J 1) Confinuqd. Mympfohflsi 4- Number mt: agympfifi+eg : n—m : # FOLES F # ZE‘I’DS : 2—1 2 ‘ flI’WBIE 01f asympi'u-I-es : $549 : '80 + 360 (JELI) me h—W‘I A : hi! r [Pa-m) 96L flhfiflflm) z mg" 1-9- Hue negafive veal D.fo is H39 asymph‘fi‘es‘. Inirevsencfion 0+ GEWPJ‘hOi—E’E' : figympbm inwrseci‘s Teal “is 0‘1“? “i, _ ZPoIeg - Zaems —2.-C+ fi~m ] ll 1 [0 ll PTflblem # LL {’17: F ms) =- I/gl (3(5) : H lDOD+L+OGS 3+ 1000 i 1.) FEE) : 2- :06 '3 +i55+f00 I closed-H05? +mns¥er “Fund-fan i; as; $0110qu ‘- 1 13(5) cc; Hfs) .: ) 1+ 9(5) 5C5) 955} r_ K (loco-+9003) I 51 [5+looa] Kfiaoom+woog_)x IOU i + 31 (3+1000) SL+IDS+1OD LeJl—a (its) 2 PCS} 5C3); ‘f‘hereForE’J, arm-[2(3) : IDDK CIDDO+Lr003j (355+ Mammal). (51+ 103+ 1:10) REQI- axis Plol‘ TEE PQHES ave 9+“ Gyfijfiloooj —-5 i'E-QG: The ZETO 1-3 {If «S .: -IODO/g_rflo : -1.5 Remember”: @1331? C‘Gnkfibufigfi CGum}: Conjuafl+fl Pole: is 313:0". .' along +‘v'e, x‘flfis : Does 116+ exigf- ' Bemeen C: and 4’35: D0695 9.0+ existaince angle. Con+fibgfiefi 1‘s 360 + 3.60” 2726.. Behueen ~25 and ‘15-‘00: Roofrlocus exists, since angle. Cowhibufion f5 360°+ 3605+ I80“ =<10o°. BEWEEE ‘lfiflfl and ‘33 L Roofulcmuj does 001* exist sincq qngfe Can+fibufiofi becomes 3€Da+3600+igflfi+lfiou. [Remiemberj H: +h€ {HUMBET mt Tedd P431185 '1‘ Tani zeros am fine TESM— ant Hue ‘}-E.sf- POEM“ odd I +hen “Hm W I’MM +E5+rpflin+ ES Faflf‘t CH: H‘ae Toad IGGUS‘] Iany m Phi-9.3 * Number of- asymp’rfi-es 5 firm = 5" 2 1+1 ' Angle; OF asymp‘i-ojres : (#3: £th + 390 (J34) hm": Wm CI u. (3 to $51: H52135_}22.§;315. In+ersecfion 0F CIS):.W‘JF3+D+@S (xiii-h Tami axis 1 c{ : ZFokes # Z zero; O+D‘[DOO~5* 5 ~ (-25) q ,1.) [GO FEE) = 34-10:: KClDoc-l-HQQE.) H“§ : C) 52(5flaoo) Kilo-1:: S c: 1 + l {mi—trot: J x I5 a CS+IODGJ 54-100 Q{5)H(s) _: IDDK Home + 9003) SlCS-f-IOOD) (5+ loo) Real- axis Plo+ Poifis me :11“: S: 03% ,-!oco ,—roo ZETD {a (if ' 5 z —. 1.5_ Hang “We WE}??? '- Pnoir lows does 0.3% exisfi. .Bahueen C3 and '" 2'5 1 Does no} 9265+: flare angle. Confiibufion f: 369:: Biween #2'5 and “'00: Rib-3+- rOCUS EKESfl- Seweea F100 and —|0001 Each? locus. doe; 00+ finish .Behueen #1000 and -CC' : Rafi loads exis’rs. . fisymp+o+€5 number an“ asymp’rofis Lin-m : Ll'l 5 3 finale 0? asymphkes 535.19 = ‘30 Jr. 3’5” J1“) h~m fi—m I— Whem, i3 = FIE-,3 In+e~r59cfion C‘HF asymp’ro’res. Lui’rh 1*qu axis I : ZPoles — EEETGS 0+Cav-looo-‘IDQF- [Fl-5) 1—.- n—m 3 o( ,_ "zeta 25333 3-) H’s) : 1 (its) Hts) : F65) C(S) 11(3) :- KCioao+qDos) ‘ | 53”" (5+ r000) Real axis pled- The Poles. are CW 5: 0,0,'|0fi¢ The Zero 'rs at 5!: "2-75. ' Along +112 XfiflXis 3 [10qu [mus dneg nefir E265.“ ' Be’rween (band: “3-5 1 Eco? locus does r101“ ERIE!" - Bfimeen "2:5 and €10“ 5 Roof“ focus 6x131: ‘— ~ game-3n #235 and ’00 1 Eodfi‘l’ {GLUE arm ncf— exist KEN—57 m Pf‘o‘f'i? S ' number of a§ympfofes 2 fi-‘rfl '3 3"] = 2.. . finaxfi OFF fljympm}as : 96$ : 130 + 3’30 (J34) ln.+ersecfion oi”- cusymphnfes mH’h real :1fo p{ : Zbeesu “items o-J—o—IOOO-C—L-E) 2 PTDHPT‘O 1993 1-) PCS) 1‘ ., PCS) = I 3 ms) 2 kl, + ski sie k4 = 9” cts)_. k? +23 KP+23 I.— CS :.* H ) slag __ KP'i‘LS |+ Keg-23 .1 '— 51+15-«Q-1-KP Remrl'i-inj Hts) as , K :2. H03) = 2- F’+ S 5 $15—97 K H _._?_P__ 3 +2g#g Qfs) 12(5) = PCS) CCSJ PCS) a I‘4?” Ran} axis Plcaf' Poles .cm‘re CH' 5 '5 1'9953,'g'5qs‘3 TEE syai-em does hoi— hqve. tram. Befil-xuflex‘m ['69 afid +05 : Reef {MUS does fie? Exia'r BEJFUJ-een "3.6% and 1'6‘1‘ 3 P401- [onus exisfg, BE'WEET] *‘5‘0 and ‘3‘“? 1 Rack locus does nth!— exia‘l‘ W. ' “UMbEf 01c asympmfes i fi—m = 2m: E 1 . Angie of a.s)cmp+c+931 gig = [as + 3:30 (JFK) “I'm mnm S‘s-E : q¢°,27o° Zn’rersed—{on 0F asymphi‘efi mH—H Yea! axis? q; EPGIES- Zzaros 1+6Lr5$e 3'6‘1‘53 =-i n—m 9- Prehiem 4% Li 1") From +he given 1130+ lotus J. —Find. ou+ Hue {ccqfioq 0J3 Poles and :ems, The Poles are CH" 5: Fats“ :: rug The zero 1'5 cfl‘ 3:- “Ll Thig Pmbfem figseanH7 is backwavds. when Campnmd previews Pmbiems, i-e. Elven Hie moi— lavas. we. need +0 Hrfi H19... HansFer ~FLJfiC'r1'or} L(£)_ Conraf‘rucfifij LCE) 'me Jrhe Paleg and zeros 'F'Qu‘nd above.) L._[s._) :. 5+9 r- Ans (51+ 4'43 + 26!) (5+6) 2') Dmo Jrhe. cane in comP'ue-pec. quna Cafrespflfidffifi '[D :3: D‘Lfo.??_. Mm. Hm, ‘3 2 £5515 . Also, dTfitl-O a dchqu curt: Lui’t‘h “(wilqu 1‘- L01) {-9. *mdfua = 3-63. . Hence, .H- can be Seen -Frorn gloom ¥Ffluve Humi- H‘ is r101“ Posfiibie {cw H 10 ham dump 11713 val-1'0 3T£fl+EI “Hum _ _..C)' 9&1}. and, Hula If 3'33 :.. "k 07 Y def ¥>A&Z deYOX;(\/\€CHOV) T of M 0“ g — 0’055 : “1% 1—— 0055 - (sac) O’O‘Ss "‘ W z “7" ‘VQ ’1 4— 0‘05" S ’ $ +LO 4-0095 4—,(30633) ’ am? Ow de apwuxfm 33m 1 :2 2.‘. ' ’1 4 0063 + (9:153) 12 1—— 0’0? 3 + "019129;"L 4+ o-ogs + °OO1L€’§1’ 2V .2 swim—p850 ® 5" + £10.; + gOo V N 0&2: K N. @CH’MA‘ Pad 2’ app/W‘iwvx’f‘ ‘iS —§‘WDV" Mr" is \ ‘m fid, 3V_ 6054—1100 9A“ 44» WQ'4MA fix, sum 60; «L (LOU __ "(r/L: Q/ovv’pwkwg A“? k WVVHA WM Mvdvad. va‘l‘ 3T5 ,2 "a! ,2. é V 5x18 "0x ("OK Wufl +133“ F5 \ flour] 0%“ I 3% 2 and 4‘s wmok 2w,ng +9 CAMPMLQ .MAAK 4w: PC" «— s/L 0\G+U~0\ Fade, OAQ‘ yupflion. ' So 7 wx ‘fi’fic‘k Ah) :Qmw . 2W 6. g __ “7,9 —— S 3v “Q” 3‘ £— ~ [l‘gnin-‘Z 5" z‘wz g a W 2. ~ (him) 3 ’1 Jr 8+ WL 5V4. zg+ L ‘ " <1 .1? &M :__ 1~§4~T+37 5(54—35V_és46 ‘2” Ci \ ' :2 0» iv ,2 5 W (‘ 4 .43 +A 5; + (a; 5% 1.5"; 65+ 4 j 6‘3 6(3): S+2. E 0'55 s’qws + g } Shes}. 0\ 4H“ DVQLZJL QQP‘roxi‘M—{n‘w‘ US (NQ _ ,/ ‘ NM 4 ' - 0x de “[de apprufimkhbm E— 03“) News; "A 15‘; . r V £ 3 Q A 4'. gs’v -153 (\— -: _ #— VQ’ \+ 0‘1"; $ + Q4535" gv 4W grep. 32, L A ’ r as} .2 {w} < <1— gsu. 7,2) 354., S“14m gs+ 31). 1 2: ,9? K c? ‘2 (4C? 1+ EO'OK; swo s44 0505*“ 100p pow m WATT} o{{” \+ k LCS): o «NW/L2” LU): Sgt). E o as s A WWW“ Wewwwfifiom {3+ (2)5414) Md "k'b a 95) r u x Q fix" 91:3 “was «wk “WWW‘HW oz? 2 L,(© and 50 +0“ “0&3, (Lr—B 00> (9603 ...
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HW8_sol - Problem saf- g Eofufioné PTDHEM =2? 1 a.)...

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