Exam2F04solutions

# Exam2F04solutions - ECE 232 fall 2004 Dr. Glaser Second...

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Unformatted text preview: ECE 232 fall 2004 Dr. Glaser Second Examination October 25, 2004 Honor Code Agreement “On my honor, I pledge that I have not violated the provisions of the NJIT Student Honor Code” Signed: Date: Name: IDnumber (30 points) Problem I: In the RLC circuit shown below 1205(0) = 0 volts and it (0') = HI .4 amperes. a) Apply Kirchhoff” s voltage law to obtain a differential equation relating the response verb (1‘) to the source 120‘) . b) Find the characteristic equation that determines the source—free modes. 0) Find the roots of the characteristic equation (i.e. determine a, (00, and (ad if necessary) and write the form of the solutions for vab (I). d) Solve for the complete response vab (t). R=2 L=1l3 + v(t)=5u(t) c=3125 b I<VL Warm too? Vii) 3 Va 1‘ Vt. *‘ Wt,- " LL’R *Ldﬁ “rub- (her , C(pqwﬂ M 5 Mr“ 60 AW“ M We): LC, Mi?” + 11c A?” We of MUM, ,r & chat, + L. Uh, : 1. 04+) M1. L M \_(_. LC. \I ‘56- Lel’ we” éom‘ohatpﬂe WW‘QJ-ZL egraﬁ'uon be Best 42““ A‘VMr/M 7’ shed 3 (Pay/M": 6v MST” Subsh‘tw‘me’ “Ar-o "(Rn-e ﬁcmm-Qﬁ“ ewon '1. t X"? - Pix-2“ :z-Jw = ks‘ﬁiwhw =0 1% 0Q“ 647* ’7 e- \ \$ 6 M implfr Mon \ 5‘ *15"1'.'c.=‘3 (L3 Du Jt: —=o°° 11M “mm’t MMVOW~¢wk Ann‘s Lo 0 3 go 17;&_kt-W\ =\L DASO We. er \9 he am ow,“ WM Om) “9nd— wAMov be We a \$\wr'\ mm "at: K=§ (‘ﬂ Vad’c)" 93ft \Qws qt +51...“th + S Ow} ﬂaw): m»: =vwm-3 =0 99—: {3‘5 -.-. 3593* \Rm Wt x-Bsm Wt\+ éat\~—-L¥Rs-\M—\‘h +\-\EcoN\-:\ .4 'dﬁﬁqu—gp‘xwgq’c —(‘3% PJQBSInLK’C‘ (20 points) Problem 2: For the waveform shown in the foliowing ﬁgure: 3) Write a description forﬂt) in terms of elementary functions (Le. steps, etc) b) Find F (s) = 13[ f (1)]. Note: 19’ you can ’t do part ‘a’ (and only if you can ’t do part ‘aj ﬁnd the Laplace transform of f(0:u(I—1)-(t-3)u(F-3) + 2(1-5)u(t-5) — (f-6)u(t*6) + 5(0 for half credit. Kt) 2T 0—) W) = mutt—o *Swtt‘m) *'Si_(t“—)WK’C"'L)-gi(’c—L-Quk’<.—q)—L\L({- '1. -5 B 4. 5/0. -ms / Ms 3 H Ftﬁmum" 3‘6 -‘53 \$+Ex£ —%e sq—ge, -S -3 _ _ RYQ PLS): lge’ ‘ ‘E‘me’ S+§Cees “be bs S; (20 points) Problem 3: a) If F (s) = .8[ f (0] show that £[e'a’ f (1‘)] = F (s + a) . Hint: Use the deﬁnition of the Laplace transform. b) Given that B[sincotu(t)] = 2 2 ﬁnd the Laplace transform 5 +0 of f(t) = e—H’ sin 5(t — 2)u(t — 2). o.) £12m]: gimme-5‘»: -. H5) 9° EEK-64Lth t j—emlmﬂéstax 1 I “He—(3+le M a- = ¥Ls+m3 ‘b3 git»: e**“”.mhskx-mxuxt-ms \s a\ at; %onn -sL \iﬂ : 3 Sm Sx \LKuB WNW“ \L = "C'm m ox. now-Me" swit- o‘nsm TXJ la“! in) —. FLs-u) o a {ﬁn QVLU-kxj: [6+\)7-+w1 Ls+l)l*5‘\. ‘ L03: We MQ— SKULQK Korwwlb B an ‘—-—"'———"‘ e -Lt-O \ _ u “L 1 I 9. Sm 5%. a) [’t \ L5+lyhk51 3"”.3 +3.19 (30 points) Problemk Find the inverse Laplace transform of the following ﬁlnctions: 4s2 + 9's”!r 4 s(s + 1)(s + 2) b) F(S) = w s (s + 3) 432 + 155 + 89 (s +1)(s2 + 43 + 29) 81) F09): c) F(s) = :. _________.._. — __ ____... _. \3 ' . M Y-KS) _<.\5*‘)ls+1) _ 3 4' 5-H + 5n. Wt Fun“ 0‘ PW?“ malnoan XMA‘OMon \.\ i : — -— 1 is. 5mm“) ,L - ‘-\S +‘ls1—‘l\ q‘q*“l_—_l_ _ B. KsHBFLsﬁﬁh-l a 5"1-13 3-4 1 \-"L ' ‘l ‘- \ l ‘_ l—ls"~—0\s+\4 _ Axvl -\'8 Ht :1; 1 Ca?— k\$+QTL55\5__-'L= SL+5 \s=_:;_ \-\..r]_ - 'L \ Smkﬂi'S) .. p“ 9 FL. " "E73 * ""53: J’ 5+3 “\s‘ + \5s + ‘Eq _ , o) \$K5) = W no “\Dro‘ﬂA Mlomi Quad-Ion 54-4. '45 + ‘1‘} = LSPLT" 4— 5"" \$ 7L unﬁt/)4 Omtfujaje 730k; «I 551: —’J. :38 \k5“+-\%s+%‘\ R=k€+\)FKS)\\$:—\ t. gags +11 \ “cs‘msswaa __ _'_3___ A? B3“; ts+\)K\$1'+'-\s+'z.‘s\ 5'” Sﬂ‘Msi-‘tﬁ ‘ ‘ QslHEsa-‘Bﬂ 2- 3bh~4umﬂ+ k35+¢)k5+\3 ‘= '55" MM + 3-? + st+k3+£35 + C. =5“ + as a- 2.\ = Es” x—(B:+c.\‘5 +C. Egydcmbl wﬁv‘AWv’n a\ ‘5 M15 P)“ Q. C. 7-1 50 5+3. -\ 4 .5 avg; Vb) 5' l + k\$*m)u+ca1. .. t 3.. \agta— (2,1 cos Et\u\’c) ...
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## This note was uploaded on 02/18/2010 for the course ECET 232 taught by Professor Gla during the Spring '07 term at NJIT.

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Exam2F04solutions - ECE 232 fall 2004 Dr. Glaser Second...

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