EE303_HW solution

EE303_HW solution - EE 503 Fall 2009 HW-l '01-; c+ = ‘ '...

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Unformatted text preview: EE 503 Fall 2009 HW-l '01-; c+ = ‘ ' 9H),. 1 a i _1, “(up 74 , 0 .00 l 3 2 E : m? ova + 1.1109: — HI =2 .9 0 ' l mLt)+gd'7 1¢3+gc+)- i9, OVA“ 9 0, also 0 1 2, IHS? 9561')..9L{-) - 0,5155 2 : Ex_9~519 01+ -H NT Ex, = y sin“: (if 0 awe Th9 "d‘enfify (03 (“Th = 505” " “flat = l " 93"”2't , 00% 981’ Sinai=l (L— cos (21:3) 2 QTY EL ‘5'“ o 0—0330”) dt s?"- 31!" “g [a raw-ELL cosbbdt 211'. = 11‘. .L [.1 smcm] a 2 o 2 TI _JL.l [Sin Cq-u)-5in(o)] =1r.. 1% [0-0] E :1T 2T 2! flow :21 0 5mm + 1 OHKM xc+y+9c+7 = i 0 else E 2"- . 1 I‘M} : So (Sl'nd') +1) (it = 5:11-(51'n3d') + 9 Si‘nth 4- 1) (it ' arr air a = L) smdc) 0U: + 9 £0 smcbdi+jo 1 t “ha-mam: mu“ -_ w + o + 91F 9T]— 1: 3 h m “9 Silt” — 1 Ofl-k‘f 21f “LLH— l5 (3:? , 0 me m a E = j (Sim.th — 1) 0U: 9.1-9] 0 1r 3‘ .2 S (Sagan Fa? amt-b) + 1) (if 0 “T :nr 2‘!“ ‘A' 50 sin-200014: -— 3 J0 SinC-E) oli- + £0 .1 (ii 3m, 1 01mm 0 We, m {I L..r-\ at 9. 3 3‘ 53:. II J. 51T(1—¢OS(2+))0UL I: 0 11' (+70% 2 0 .fi .LS‘VLCD‘H] géfl-g-[9I o .. 1r .. _L [shunt-5mm] "3 H E a 1 oH' ,. T 9 L, xCrJ-tgck) finch + O {- %Lf3+gci);i 1 {fin 0 we TF . a Err/+9 - IO (51nd?) +1) 0H 1r Tl 1" _ .2 . 1 alt _ S . IO M atde + Jo ammou + jo 1T : if- 095%) a "" a [ ]0 + Tr = If _ 2 [mow—mam] +11 3 = II —— 9 [-1 #1] + W a s + H 2 E 7'” : a1r+s .2 SF‘rLL-EJ-j, gift «If xtH-le-E) ,, f 0 UL”. E 1’9 rr = 5’ Sinach O .. 9 [—CDSC'II)] W a : J’O (sixth—1) GU: _. jowgsmmouf £1 (it 1r +17 0 _ g [.(pscrr)—- (—w5C0))] +11- - 9 [fit—1)~C-1):J+T - 2 [1+1]+Tr Obsa'vodtron --md,e, in Part (a) Is Owl: valid. Iawmore. We conclude "that; in gameer, Ex+y :rL EJG + 59 or 2,6,9 #- E3459 . 1.1-; (a) mm = 5+ :0 0050001: +g) T 2 P : hm J- I/2 I; + :0 C03 (roof +110] ‘7“: ' T->cv /2 Pk = lim __L, f /2 [as + loo Cos C100t+TI) 'f‘ ‘00 £03000“ng )1 a“: Taco T .173 3 7?: “7/2 T/;, 9 [m J- K :00 cw CIOOfHV/i‘) “Lt T-éw T —1-/9_ I P :. 95 + 0 + h‘m .L :00 {T4, J_ (1+ cos (a (wot—14173)) OH' 7‘ T900 T 4/7 a '5: 5 T6 ) 0H : + km 59 f + [1731, -"” J (03 (RCIOO'b-I'Fé) T909 T "T/p 76a? —T/D P1; -’- 3'3 .1. 5.9. 'T +0 5 (b) 7;“): IO cos (l00t+§)+15 5in(:so’c+][) @ 3 P76 P76 = lim ..L (T6 T->w T “V; :hm ..L T—->mT "V; [lo 695 (wot +E)+16 5m 090’: +117]?- 0H: 3 _ 3 [:00 cos? (root—HE) + 9% sin? (Howl; )+ a 3&0 cos (mot+g ) Sin, 0901? +1; )] dt 17 Tea) T “1W5 (9C100t+fi)) (it + hm ’33 7 3 {2(1- Sin (atlsth/afl di *1]; T-—>ao T «j; + 111% IE). T T T [Sm (mot-r1; .- (toot +33 +Sin (1501.5qu- (toof+§))] d-t “900 " a ‘70 _. : hm 59, {Ed}: 4. hm [53 [ (93(2C100++1£))0L‘l7 4. lim 13:9 T9309 T "/ Tad) T ’90 T-aa) T ~17:l 1r/2 1'50 + llm _. f Tam T r172 5m (go-b) 6!: + I..— I9 cc) vac/1;):-CIO+25I'?LC3‘I:?)C195C’O{7) = IO (.0: (tot) + 2 51‘10t2chlot) :10 (.09 (lot) + 9.15 [51-n(“_lot) +5”! 0*“on x c’c) .-_ ID 0050019 4. 5m C—H)+ 5m (15+ 3 2 .172 [10 cos C10+>+ 5m (Jr-t) + sin 05%)] 0% [loo coszClot) + 51"»: C--'H:) + SinzClat) + no 05st t) Sin C-‘PH+ 10 917.41% 7 cos Clot) + 2 sin C—H ) Bro—r.th 7'] di 7/2 7/ = lim _L 9 I . a co 4:) oLt hm J— i 1- SMGNH) 0“: + [T 00 .él(+ 8(20 ) +TawT _T/Za( hm .L {123 _1(l—Sin(zc{:))ol.t + O + 0+ 0 ‘ h CW< know ith flat [oust three parts will YCSDLH: m, 05 became +6 - S‘nwol‘d’?’ “WHPIM 01‘ Sing omd. wsiw com be writ'fe'n CM Wsum 01( I 0‘" 1"" PWJ‘ Cb) - Sim ‘Uw iw’cegroj. of sfmaorou over one period 19 J Lee qc’c {61/065 {Or "the. {mi 3 Bari-3. T/ ’1’ 17 P36 =1i'm .LSg-Jo OH: + hm .1- [/2 5‘0 wsczoh 0U” 4—“me g 2 [at _ T—awT—‘g Tam T J73 ' 'T—no "172 T T . W i (/3 9"”15-“4’” 0” + $7” i1r {T6 i 0L,” 2-16 600 *6 '- [4—5 c d.) 'LLH; lo C03 (5%) gas (:01) 7/2 P1 = h‘m "L f (Io cesCS-thosCmH)? d+ 7—9001” “y: : lim —L [v2 [loo ws’CSt) asa(w+)]df = 11"“ J“ [122 E00, é (l+ms(:ot)>--g (1+ C93 Gowjjdk T - hm at; I 6' [H (moot) + (05 (20+) + as 00+) cos (20+) (it T900 T __T/2 T 'T/ Al: T / m2? 20039.0” :- [rm 535 f 6 OH; + [Fm-9‘5 [2 £03 (lodel‘ +1.; fgyz T950 T 41]? T900 T -—T/a 3“ T/ +lim '2;- L: (05 Clo-E) Cosmo-t? (ii: T T—am T /2 P95: 95+o+o+o =95 Rmsszzs (a) ma; 4:. 10 3m (5%) to; 001-) P = lim i- gT/a [105m (sinosoo‘cflldt x 1-9ch ~17? : [im .1. Ta [I00 51n1C§+)wS 0017?] d)“ T—aoo T .1); :lfm 35 Elf/1 (laws 00%)) (1+ GONZO“) CH T900 '1' :51; T .- H005 (7.01:?) (if :‘im 3,2 S I? (I -mon-L) +cos (7.0%) 05500 F’T 1; T4’ T/z c 9 (20063 . o _ ['rm 25 172 CH - lim (‘35.— 2 COS 00*:de +197“ R'Ts: [-172 T ._ {Wt 35 S [2 503001) cosCzo-k) cit 35~o+o-—o myth; @45ng ll !.l..9' (1}) watt): 6 (93, 1.1—3 Cb) 14—; C00 mt): 5+ IOCGSCIOOf-i-E) 1 No’cc cw 9 z 1 (639+ 5'35“) : 2 ' i; 11- vJCIoo‘t-i'Wé) ‘ and; ;5+IO [2 JCI°°+/3D+2 ' chIoo’c-fTVj) 2 5 + SEJCIOOthV3)+ ,5 a - - ' ~éloo't) m3 float) + 56-31% CJ( 11+) =5+$e 6 Using 'thg resuH .[rom part (a) . .' 9. ,_. cW/alz + 158%] : 35+25+25 *5 P9; = [512+ ['5 EMS a fix} . Cb) Gui) z IO 095(1001' +113: ) + ,6 3m CISO++WgD = 5 63(100t+1r/3)+ S €3Cloot+1v3) + rm) : Sew/3 e'JLroow+ 5:319; cfl-Iooi‘) fl 8: elm/5 J U33“?! {he result from par-t (a) ‘ . 2 PW Wain/312+ lse’mlzJI- l'gjfij-wglzfi’ lajc’mg I :: IO--]-- 1 ( J - lat "JTH: fit -J|51' - 5(CJIO't+CJIO‘t)+ J— (CJ +e’ _ we 1] . 3H _' , Us”: o '1” .l ‘0 “ JIOi’ JIO‘t-‘J‘le __1]c +2] 11.7137 58 +56 1 2 - ‘5] w .I J— —- Pk: 52+51+fi+fi+fi+q KMS :{gm Lt) acct) ; [0 Sim Cst) cos C1017) 's+ 45': 'mt mot) = |0.J—..(8J «e +6 2] 2 . 515+ —5st 35’: 4m) acct) z—EJC +3 -5 ,6 2 " 2 .5 P :. ‘1 I—Sili ‘Z; (f) and) - e, wsfioo’f) ‘t ' t vwfi z a” g (Cm + J ) Jfld+wo){ l JUL-wort 101'? " £3 + 2 2 2 3 J. . P2 5 :11 + 3% 2 . I = E KMS f; 2 1*9'5 Ca) 2%C-5t+l)='t (mortar-memo) what. butt) 1‘s (2 wm't‘ 35c]? Jumh‘on- tut) __1:_vt o I BY Time. fizmmoJ act) Lt 0 By. ‘fi'mc' Shifliflg u. (—1") 1 o 1 .._LILL.4_4A_L.L4_...._‘.. ..__ . ___ l-J—ELb) “a ("fit-H) r, J: (uct-u)-utb+0> ac Gal-+1) .—. 15 J; (uC+-:).-u,u:+13) t sivu‘H 0’} .1193 is ribs, (fig/3H,?“ Sm {wowed 195 (origh 9c C-aHI) - ...
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EE303_HW solution - EE 503 Fall 2009 HW-l '01-; c+ = ‘ '...

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