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AK-MATH225F09-WS11

# AK-MATH225F09-WS11 - MATH225 Fall 2009 Name WOTkSheet...

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Unformatted text preview: MATH225, Fall 2009 Name: \ WOTkSheet 11 (6.1-6.4) SectiOn: Se ’ atla 6 For full credit, you must show all work and box answers. 1. Find the Laplace transform of the following functions: ( “Rog MC? L)S(_ (Jag, Eab L1.) (a) N) = 5 3051:st 53(er SK? 3%! ‘ CﬁQ/FCQ (b > g<t>=t2e Z -Z:L :: Z S [‘t E, J: (s _( '2.))2:H (3+2): (#9/ n =1/ q:’2.> (0) g(t) 2 3t — Ssin(2t) fCBt"Es%ian" gods E§§E9nézoj 5(Cﬂ) Séég) ( #7, "7—! .°F WA?) —; 3 _ lo 32 gL-rk; (d) h(t) = U305) cos(t — 3) x “E 5 [u3(t)a>5({; 3J3 = c 53 [coscwsuej :c ELL-8i , H: 3/ 0‘: 3w: (ojét3) \ ; Cf+3>=¢a\$éﬁ3 3 “J—Iﬁzlo/ 5:] (e) W) = m (01:2 :[UML‘6)_LLJ 3 is 3 [Unﬁt] ; C':§C tz+zt+l 1 ‘H 3 09,] )Lt):tZCSZc—,3Ctl*z,Sgﬂi1+¢€3q§(t 705% (5’52 - ~s 2', 11“ *S \I ' C 3" '* 2c.\$(\“j'c 1>~o ﬁﬁ/O=Z »~-———-———-—2——-———~§L_—w / \ __ 'S 2 \> .\ ~S Ex 'SKJ d_‘3=£7,o;l —— ‘5, +5; “524'“: sj 2. Find the inverse Laplace transform of the following: 1 a) F<s>=— 1 ( (3—1)(s+2)(s+4)l ,4 HS): BLQT)+?'.{5TL \ V Jc‘aﬂSi———~—=__§.+C— iii—1:;— (s+Q(s+Z)LS‘fL1) 5H 2+; 51?; .5. A J; (37%,) (a ﬁl-l = -—I.¢ Angrz/VHLQ +B(S~+DZST ‘4) + C. [ls-Alﬂs-tl) | 4 532', 0 #501502) +ozl / B :2 S [’75)]:1566 war. 0 +o+cC 'W / C’T -; .1- -—l: -?—-t M 1m: motswowzl / 6L 3-; 3a ' N (b) G(s)=s2+23+3 .__.__.... 5 5 1 ‘ - ’r ~ 2, ; V L t) __ :_ _. 5 Mac. :4 HUME) 0/ 9M 6 Packer 5L3) (m (\$10,72— Cam (Ca; '6 C. S Aloft; '. _ [—1 ~———€—-——-Z'-—‘ . - \$+l JL 1 \$242.5—f3 =7, €3+Zs+l~QH ija CACS)” Ls—rd’wz Ezsﬂﬁz = CsﬂW—AZ 33 _ 2 ‘W'WN‘KNWW (c) H<s>= W +4) 4 F ' ”s 2 A 733+C; V -_ . Z, . . L SC\$L+T1+ 31+ I», . , H K\$> L! S [F]: m- ,V }[\$2"—|—L01+3(%S+C.)‘\‘ 53 ZL ' ' H . V l l _| S} 7+ 3 Z/ l és>~ :(EN Jab. ‘ 572. , Ash-AHA W33 Ads :35-21 < ‘ 4+6 IO (“33/ L14; ‘Z ‘1', 6/ #C/ 91:0/ bk '6 A: :/Z' 1* )0 if?) :-/4;:L _ 9.: J. - v.. (4&5 ., t?— ‘ Z ‘ [HZQ] HQ 7, ‘21; V_ .. .-_ ~ ‘ «”f ‘ ‘1’: ., V +97 CoS(Zt + —3 510(ﬁ) ~ ,, ' Ada \ v: +A¢¢>51aec5+~gsa¢2g F' a ‘ J95... _&__ é. \ I A! k L sis—0 S + 54 7L (s4); A ‘ A [5le + \$350 +C5 ; 3 “W AdsEZ§+Q +8(5Z—\$) +(s;! j[\$) :ng 31% f 3"?! + (51"?) A+B:O ‘24-’8+C:O A2, \ - _ - 04: Bl-A (fa/H8 S‘Es]“c 1’ (”A/“:0 1‘ .. l 6 \ C12": S ‘lsjjzc’. (HTC/ a I) S" [m]: (.675 [FY/OH/WI) = am) A ’ ‘ccé'z’hc‘ﬁi'iaﬂ 3. Solve the initial value problem: 1/ II—~6y +974: I, y(=0) 0, y I=(0) l (3) Using Laplace transforms aggreig] +739] =30] ( A1, AAA/Ac) 3 3973 37“) 7(0) (£55991 7108mm] 3% 57-891 ~I ~esac7] +c1 3C5] - 3‘.” 3C71Cs »[¢S+‘ﬂ = g l+i 1 1 ,__I_/ +\_ is») 315 Aw) 4“ Am séss)" 83%“? Alsw3)l +l%s(5-31)S +:C5 >1 " Aa’s 43%) A 615*35)+C\$‘ ' ‘ 4+3: 0 >(Z143381’CEO €74?) 6“ a»: :AABB A>~’ (517:3 (b) Using the Method of Undetermined Coefﬁcients. )AZ yhlI~vah #17150 /7A:C 4. Solve the initial value problem: 3/ + y = 1 + u1(t)(t — 1), y(0) = 2. f [7'] +391 = 301+ SﬁuwH—sﬂ sﬂﬁvﬂa+igy:mgﬂ+éﬁ§aﬂ‘ 33£71*1+3L712? 'ILCS S[\) és+l§§£;1:z+—§ +C 3%) :£,71 ; a-r—‘l + k +C 3%) MW, at. W; 35+!) W ':ﬁdﬁ :4.; 38+!) 5 EM 5 3+1 H€a4§+€bzl 5»: o ~B=I /8~'I mot 4+0211H3, \ -— ll [3, ,L v l l P ,___‘+ . ,7 .\ VI L' SZKS-HB 23’ 52' 5-H E + 3L 473?, Asésw) + ELEM) +CSZ; A+<:Q A+6zo &:J c=1 H1“! 5. Solve the initial value problem: y” 4-1971-1403 =4? + 52 (t) + 64 (t), 31(0) 2 1, y'(0) = 0. 3 £7 "3 + a 3C7] 7» (0 ﬂy] 4739,11 + 5 [gm + 3 Est. w] 17 '25 €13 C71 '3 7b) —; me) + c [5 39] 7a)] +zogig73 : ;7 +6 +55 (FF |/ ’ié/c‘H [its/ﬁzﬁu 61-5E7] ‘3 +CCSSC/ﬂ ”']+10§L}] : #2475226?“ K§Z+é5 +[O) 3L2] t 5+(D .4, ﬁ '25 "L45 5-: 7L; +6, 3C7] : v—Slc 4» k V25 \’M_ _4_ 5L+és+lo (5'!)(SZ+GS+!O> C ,‘azivéswoj ”L-ls l +11C .1 i ’ SLJVf-QS "Fl/‘5) P P \ l7 » 4 N V V é'UKSZvLQsHO) ’ ﬁ + 85+ C r ““1— +L\7_ a 5'1 s¢+é§~tlo 5“ szﬁs‘sﬂo Ads +95%» + Casi/954} :7 L AC5 +és+lo)+ 651+¢sr8yC£ l7 #ng M +c~8=o 104—0717 334’ <94+1o4a7ra§o C’=)’o/}~J‘7 B- l DA¢17 010-0 Fri} ' c: ~7 (,5 ‘ 2+ ~ 1 s (ow/o \ e +65 +(—C§)l+,o-(%?- {DZ—macaw) ' 6 3+ 391+: (aﬁ’ﬁé'é' ‘TCCCLLOP 3+(0 l 3+7 - 4‘ - ~23 l ~95 I 3C7] (9,301+, 5" (s+3)‘+; +C £543)‘+;)+¢ @1391) 3C 3 Z V: -I ~23. ’ \LI 7 (S'f3)l+l 4' 3..) la (CSwBQEH) +C Ssttsf-H) I '55 - ., _ '3L2E‘L1§ ”' = 3 T‘iCﬂ] = *cyfsht + J“ +Uzlt) c “24%) HAM): 5701M) (4:: > ﬁzz. :4 «=93 ...
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AK-MATH225F09-WS11 - MATH225 Fall 2009 Name WOTkSheet...

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