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245ch6testsoln

# 245ch6testsoln - b-b-trrur Grd\Cs"llD o ro s ffi s r'4...

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Fall2007 tath 245 Chapter 6 Test (14 Nov.2007) Prob. 1. Plot the function/(t) = tu(t -2)-2u(t -l) ' S0rt.^ |4otkt, \$tu = (t+)trH-l) + lutt-x) -1uc6-{) 2 Prob. 2. pinZ ttre inverse Laplacetransform ofthe function F(s) = F# * t\$\$., g2+4g+8 = g2+1'1,g + lt+ 2" = Ste;1+4a Tfu^^) -'t -{ -4 -) r(or=iTn,t=i'W;t =f fffi-ro;h{ =2d"{ cAsrt - u;stt t utu-tr

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Prob.3. Find the solution of th3 following 1"-order ODE subject to the initial conditiony(0) : yo: #*or=lcosbt+86(r-c)' fd}r{ t(o l+{","Trn ^sf"''t ^ + tfu oDF d4Ar SY6r -[o+aYat = A ;ft, +Bdsc @-B#+* -{ ^ -SC^ iil f ) e .f= 4JCt-c) r 6/ I €,+eJ irD --. l-,\ : l= * +* = Ao918)+Qsru\6*o) 8+tr)6'rb9 s+a. *+-t6z @ kc*,p*ruut"!.. = *(1.+ M) * s (aMtN) t Aobr+No. €*\ (53'6') fr [o+M=o + Ao=-M S{r oM+N=4 1 aM+t'J={ 8o: Anht+Ne = o J -fu +aIJ =o o M= -Ao = ;.*; N={- a-v= {- #=#- flq^c,J-- 9. =- a.--J o' s
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Unformatted text preview: b -b-trrur Grd\Cs"llD - - o+ro; s* + ffi' s+r '4'+b' *bL ; a,^A iTful = - fuao* fu cxsbt .}ssilbb g'o.Ct'c) t o"M+qN = o' ( -g'ul *' *r =.o xrrtlrncl: @"+b)U= d-+ B,^Lt. ..qdacE^") SdAr.-flrt)= ([,- #)ed* #ersbt "#s;ht Prob. 4. Find the Laplace transform of the function y(t) = 4e-2'u7t -11 ' ?rryiir" -+A" Q^&A 6/t) o^ flcul = I d2tutt-g'= 1 A2(L-D -'tct-,) = I A' ucl4) A,''t4. b&, &er*J = *; {{urc^o a2\$4)l= S [1rr,to, Ynl = t{W*l] = +{ Prob.5. Find the inverse Laplace Transform of the function rfu {r oliYo: ee,^bt- vltWo,^ aat ye: = AB- y.-]-g+2 s+{ e3t Afs+ {) + BF+z) I'(s)=#;, d3t A= ^1, B=l t*1o,,A.;f'n}',>l fudars' 6^+^u .^^.toAt il;\: sl, SO,-3J e 0,A trt) = i'lyo,1 = 4rcr{), ('-'l uc.-t){rtb-3) €ntxt*,r) l{*r.g Ysr = A+3 =6 A+?B =,1 9l-t ^'l S+2J Qr1(stl) s fA+s) + A+eB...
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