AK-MATH225F10-WS9

AK-MATH225F10-WS9 - MATH225 Fall 2010 Name: 0] 7o...

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Unformatted text preview: MATH225 Fall 2010 Name: 0] 7o Worksheet’9 (7.3, 7.4, 7.5) > Section: é Ut “5 For full credit, you must show all work and box answers. 1. F' dth Ll t sfo ofthefollo inf t‘ . U th tbl. V \ 1n e apzace ran rm W g unc1ons ( se e a (Mr filo Ora, ?Cb) t—SI'QCZIE)> (a) ggt>=t sin<2t> : awarded) _ D l u ) ‘ H H1nt: Formula 10 #:10/ 4,4 / get) = E5?” (at)/ pés) _: C 12. 52 Z 1 S fFHL} _. :; l "'l 5 5 +2 51+”): GL9) — 5 77503 C") 2? (m) L , M q cama— Lr'sfaflzsflszfi) ) “’qu _] Ll (X 3 2 > z a _ L_ a ‘ . ~ :> M (b) f(t)=e2“U(t—3) —“~ (st) ( ‘lw Cs +5. ls : S; )5 Caz 1" "llJu‘r‘B' MC + H FLS) ; S 29(11): / #H/ 01>}, W Ct) :ETEWMZ??S = 62 ‘5 fig) ? / 7 J ._ ~35 1-093) -6. Sgefl 5 ,. '35 _,t ' =635§fie E ‘66; §Z¢§7L '— (c) f(t)=(3t+1)U(t—1) wwi_510~:jflwm M PCs) = 529%): ’ FFl‘l/a‘el, 7H,) 736%., Lt+l)¢ 3Zt+z>+l =Bt+k1 ‘5 t C, 323157?le -3 ‘5 i i m‘SEBgztg+-Lzsan”i] = c [SKS‘LBWls'fl c sz‘rsl (d) 9“) Z { sin(t — 2707 t 2 27r Hint: Write g(t) in terms of Heaviside functions first. 7&2) Ll + uétirr) Csl‘nCé-Z rr) — I] :1 f + Dflt;Zfi')\Slol£’ZT/l'vfl’5§ 4‘ , #Iz ZFFM/oPZ—‘tr ) ‘ : Lt ‘ Lt) =5 (\nC‘t‘ZTi @Le) 32; gm Ms . gag“) 1.5M z—é—kc 52$Mfi3‘gb V \ '2’”5 + ._ ZTZTTS ——J E +c 5 ‘H S W (e) h(t) = t * e3t Do not evaluate the integral before transforming. H5) “’3 {tea} : git} i 2513/ fab/e : {Li’s—3) t #L‘i/AH / #35: (f) h(t) = / sin(’r)d‘r Do not evaluate the integral before transforming. 0 Pitt): l}k élfiéé) l—Hs) : game): = 33/3 Sislnig j a»; :t‘é‘)(s:|+l) 3‘ ‘ , .3, L I H» "K, £9 :3 2. Find the inverse'La lace trjansform of the following. :Cgsgg 42 G . g C (a)F(s)=32fs—1) :CS<; +5.2? 413‘! PF; (dais-1) +8 (57/) +Cg—z) Mm); + L'A+B)s + (95):! A rape: -/+ +3 no -13 .3. ; Czar-4;! 5’52...) (his) :52i25+5 — (:35(5?":Zs+5) 6Z+Zs+ ‘3; EZ’LLKC:(2)2’H(I>CS) 1—0, Do Fm! Packers 9.2: gnaw; =SL+ZS+Z“§)§5=(EZ)£ :49» :H whyufl (9) z 2 "L '55( a???) i'ééwfi ‘c'bswaa WWW 1‘93 #I? - <‘ V ' “b ) W [?Lt) ; E ‘ZGLQE ‘J 6, C EfiwéZZvué-B) 2 09/3 3.““Fi§ifi"t"ffé"ifi?€f§e Laplace transform of F(s) = m using: (a) Partial Fractions Fla) : (5—057‘2) 3—! + 572, 3 :J) ST; LE: Hés+a>+éésrll=~l 3/ CFbGV'Z WW7 “2'6: , m o \ :y : r'J‘ _ 5 a: Ems): aw) a go 6 T: l .’ B A ;. I / fl :7 3' «W, n _ “— (b) The Convolution Integral - "aé t— l _u_. _._ PKS) 1’ ( s: / f-l : G / g Zea—r; a a»; ~?(Jc)=§“%/P(s): 2 ohm: , 75% t —»z .13?) :80 ate, ( AT ‘9 t it 31‘ a g at a; o\ L ’80 6 CL CAL - 3.} a‘: i: _ ~Lt .L :2 alt ‘2}; 6/ 6 -’ a ‘ (B t 4. Use the Laplace transform to solve the integral equation f (t) =Qt+ / 7' f (t — 7-)d7' 0 S 24063.3:- iid—“E + $29k HOE, PF: P ( _ " #32416 " #:le Amywsfl) k6[$+0+US'0 {57’ S) ’- 4— géiigiflxflf 4(52-0+615r‘-/3-1‘CL§L'L:+/)=sz TH: H IP‘ 2 I / 4+5) + (8 vac/)5 +(~4+8+¢) 17(3): (34, 4* 5’; F43) L’ )3 =51 \ _ xj_ (Jr—kcg) grave ~4+8~+¢=~wo 1:5) —;;F(S) .’ 64 4:;4, g=ac ~n+c+zc+c-o ‘ p fl 33>. &=ZL C.=T.Lr — *7 i , ‘1 PCS) C ) 5 > '6 I“ +£BA=I l=¢=l|,q.=l’n; ~ 1'. B E ' ,_L 4 PS) (5:; > 5." 7:15)“ Hzgfi+bésflb> - $2— _ M31 w— H) P (5) ' (5-01524) / (5-043!) PM _4 e) .C. :75; m ’zi {3 —L,JC+—L‘t Pb) ‘E—T +[s—n)"f 6+! {swtba'Cfi/D ‘Péa "t 6’ “Late Lia...“ 5. Solve the initia1~va1ue problem: y’+y= f(t), y(0) =0, f(t) ={ E1 of; f 1 6. Solve the initial—value problem: y” + 4y’ + 13y = 6(t — 77) + 6(t — 371'), y(0) = 1, y’(0) = 0. 527”; “FHSZ; [35573 :.g§<§év’:“17')§ Jr Si§¢f'377)§ 3 it 20, 01:77‘ #zo,a:377~ SW63) «57(0) 7 «a; +5. [5 was) vygagl—HB fig) g {mam 5W5) *5 HS 7’63) 4+ +5 W5) =6“; *3“ c; Z 5 u. S +L15 +L5) :: 54H + 6W3 kagT‘rS 3+ ,Trs l , k) — Ens I \ S V X I ( ) ésZ+Hs+/s) +6 sawsfls h: $L+L43+/3) §Z+Hs +13 ; EZ’Hqc =(+H)EL;(;)[/3)<o £2; 51+L13413 = sz+L~L5+[*i§€)L+~/3~/*—§)z : ( 3%) 2+ O1 ‘ . ’ 5+9 ~T7‘S / I 'B‘n‘S I H)[S > “ ("Sivajafirfi 4rd (sq—3)???) +6 C 5+2)L7‘"i\> :___5_i§_“_._.23>l"rr53 ,L’BWSB 82(5) Cs+a)a+fi + :3 (,SQF-r‘fi +5 C/ [sq—ZY'FJJVB C [csfiffi - 5 + Z , \ v1 3 __ ‘29. x g ‘ (5+zja-H E W Cities ( 31) E Z¢s+a)z+c1‘§ *' C, «5 I"? Z 31) H:(3/q=3‘2./L33 Fr‘L/a/q;a/ Lsfi3 ’ ~ ~ +; — 4-; x 3 Ct) ; cg ’ : C CoS(3JC) +% a; 5/ 7 F": / 6‘: (7 +3; uLJc—w) éaLt-W)s7ol3éf‘fi)) 2, ) } ov>377~ + “'3 U (5317) [utmgv :5} 0L3 (i.'BT/")> L. _ __ ., ...
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This note was uploaded on 02/08/2011 for the course MATH 225 taught by Professor Staff during the Fall '08 term at Mines.

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AK-MATH225F10-WS9 - MATH225 Fall 2010 Name: 0] 7o...

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