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AK-MATH225F10-WS8

# AK-MATH225F10-WS8 - MATH225 Fall 2010 Name 65 Offer 3...

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Unformatted text preview: MATH225, Fall 2010 Name: 65 [ Offer) 3 Worksheet 8 (7.1, 7.2, 7.3) Section: Forlfull credit, you must Show all work and box answers. 1. Find the LaplaceTﬁmsform of the following functions. (Use the table.) (a) f(?5)=3t5 me» = Sam): = s s at? -= a < =}:2<;% # L-I r) = ‘3 V / (d) f (t) = 6—4t sin(t) + 6—2tt Pas) = ﬁiﬂtﬁ = iiéﬂrnfi + Eight; I | ‘ (5-L,H))Z_Hz- + W 2. Find the inverse Laplace'ﬁansform of the following. 3 _, 5 (a) F<s)=32+49 ~ ﬁlm; at) = giﬂdizlccﬁwt) #47557 V _' \ 1 a B _ _ l I 4 _L <b>0<3>=32+:_2o ” cs+sxs~~> 3+3" +541 ' ?(S*F)+ ‘1 5*! [LEI ~H3+5(,s+5‘> 2' - A (5 _ -4 ﬁt) 7 E ‘3688 5:1«1’, 5&04 / ’ca 5t '2’ _ I ' ' 5:45: 3/4 :I / A :‘vﬁi y c =———1——— -/ A E) C +0 (s_1)2(82+9) ~ 3—,! + [5"): ‘7‘" 5:..qu fEZ 4&4) (51+?) +5151?» 4' (5*!) tab) =/ A [53v5-17‘ﬁ59‘ \ +5514?) +— lest+l)(C5+D):l I 45/?— M mféjﬁﬁ} @6551} +é'2éyé +2?-2b;+0=3 L 41%) s3 +b 4 +5—zc +0551 + MA+¢~ZD> +(-ﬁﬂ+‘75+0)‘3 /.}+c“-c> ' 4+B'ZC+D=:§> §\A+C—LD-’~o “01,4 +‘7/3Jr-Dxl = '4 “W/SﬂZ-ﬁgy‘o 34'20:0 ~1/_+*‘lb‘ﬂ+_")/+;( :éLO 3:4; 0=H4 baa/r4 ’5 ‘ lo 91:1; /+:-'~ So 25' so - .L 4.. V S ; 2. [(3) His)” Edi. ,47’blzs»g)t>+§Loéaﬁ~ggz-s a; Hie) :S"§,H(s)é Ly; : --J— at +75 5% + ngésd-éésﬁab (d) F(s) 2 5(32 + 23 + 2) ﬁZ-I'ZS'fZ 1 ‘01 “L164 1‘453 L0/ be Pa.‘ actors fF‘ E—V =i+ Bs-rc ——r 5(5925’I'Z) s \$532512 A(52+ZS+Z> +ggg5fc§ : Z («Ar-rs}; + (24—41% ,9 i4+i3mc> 2/}+C:Q g t «L (j... «---2_ x1? .« gs ;_ saw 25 +2: ﬁzv‘ ZS +(%>Z+Z'(:%)Z ’ 50 1123/09. #:I/qzl/rﬂ F 9:31 7:. 5 o f‘ TF6» a“, We)? mm: W : [3+ man-F) r4: ‘3/q2'4/5H Hi'Z. 2’: #‘3/4 =~I 19:1 I 3 ~ v ):_5_ PLQJ:_ZL V! , .L _+ “3'1 l _L __, EL..— -}~ 1'15 52,11/ 5,“ ' S) ’ S 5W“ 3 Mgr! Maw Maw—twm _ “t x a bCoSt " 6, Smt ma :3‘2Fzs)? = z i 3. Solve the initial value problem: y” + y = 2cos(t), y(0) = 3, y'(0) = 0 (a) Using Laplace’Eansforms. gay/lg + 527; = 2,3305% «emu» mG/bz' 519(5)~57(0)-’;’[o) i" #13) = Z (slums) : 3:. +35 3 LS #:4/ L»! “LIL-i, b=l mt JEN/(5)3 "‘ 3595i: 4~ (:sm‘bin _ WHWwW... w, (b) Using the Method of Undetermined Coefﬁcients. , // __ 7k: 7w+7ﬁo “ﬂea/“t 7w 7? +7F4foimm MEL-4' [:0 ‘ Via m1:—\ 7 > Aﬁccsf +E>59Mi7 “'3 f % x415 +9??? "’ ~» \ . L/ ’ 1” ch . ‘ LEN") J W} 1" L (f,M-t:,c}+ yCQSt—dtspré F "1"" ‘ 7k3C, Co5t+CLS;/7t 7FH —,~ vprsfn—E - ,QLsﬁﬂ: “ﬂfaﬁ‘é ‘1‘“ lbéw‘t +" @Cast v 3 be??? t; 7:. Ci cost +CZSM‘E +’t\$m‘t (Im,syn_t %5+ +ZI€XD§E j’ : ‘CIS’\“JC+CZC05JC *s’KnJC + +ﬁb€fﬁe :zccbst +v cafe t , v 224:0 2%? Z \ OFCF—B ,7'[O)”C2'O 9:9 3:! 4. Solve the initial value problems using Laplace Transforms. (a)y’+6y=e4‘, y(0)=2 , PF ’ l = i+ i5 327': +997: = 32.5% ~~ zewsm) «m, Wm) H? 33*! ’4[S+é9>+/5£\$-M)='l I "' ' V 3 : :-~‘- 3 ww'ﬂo) mws) = 3—H 5——~' " ' ’C' B I 5 u - \‘ Sui; my; a»; ﬂay: le’é) Ids) ‘ 1+ 5.4.] w j we 7-1 2' +T'0 5%“ Tia/Eire) : kagz’) ~-L *H ﬂ; 3/q— / 0r (b) y"-y’=etcos(t), y(0)=0, y'(0)=1 <3 27”; ~ :2)? : 336ml; ﬁ-zcb> #res H=/s,aw/5;> 2:". ttﬁ,e:;,€u)=m+ P[\$)=-\$%;T 2&5 ~ \— 'Qw , r 5*} 3 / ) 57(0) 7 [#5) [a V(§) 7(0)] Fwfo 2. _ S" Hjlsl [ 5 '5) ._.l +~£6HDZ+I , ‘ W" ' ‘K ‘ L/(g) ~ 365") + Lszvlé'fZJsM ” 3(5—0 + slsz-Qs-rz) l —, A Bert; __________ w ____h +7 fl: 1 sCsi—D =é+§§r 5(51’293 5 42,2512 Pris—O-His =3 A [Shana + slésw): I 5-,»: . 3“ (A»+&)sz+(~241"é.)s+Zﬂ\$l 5=o.I *ﬂ’kzﬂ*‘\ 4+5mo ~Zﬁ+c;a zﬂjin &;»azwé, crae:; ‘9“5; ...
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AK-MATH225F10-WS8 - MATH225 Fall 2010 Name 65 Offer 3...

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