Exam2F04

Exam2F04 - ECE 232 fall 2004 Second Examination Dr. Glaser...

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Unformatted text preview: ECE 232 fall 2004 Second Examination Dr. Glaser October 25, 2004 Honor Code Agreement “On my honor, I pledge that I have not violated the provisions of the NJ IT Student Honor Code” Signed: Date: Name: IDnumber (30 points) Problem 1: In the RLC circuit shown below V3310“) : 0 volts and ii (0') = ~—1.4amperes. a) Apply Kirchhoff’s voltage law to obtain a differential equation relating the response vdh (t) to the source v(t) . 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 cod if necessary) and write the form of the solutions for vab (t) . d) Solve for the complete response val5 (I). T _ R=2 L=1l3 2i l/i\\/WW\\—? + to ’ + v(t)=5u(t) W C=3l25 J vab(t) U. (20 points) Problem 2: For the waveform shown in the following figure: 3) Write a description for fit) in terms of elementary functions (Le. steps, etc) b) Find F (s) = £[ f (0]. Note: If you can ’t do part ‘a' (and only ifyou can’t do part ‘a’) find the Laplace transform of f(t):u(t-I) — (t-3)u(t—3) + 2(t-5)u(t-5) e (t—6)u(t-6) + 6(1) for half credit. “’0 4-03 (20 points) Problem 3: a) If F (s) = £[ f (t)] Show that £[era’f(t)] = F (s + a) . Hint: Use the definition of the Laplace transform. b) Given that B[sina)tu(t)]= a) sz+coz 0ff(t) : e‘U'z) sin 50‘ ~ 2)u(t — 2) . find the Laplace transform (30 points) Problemin Find the inverse Laplace transform of the following functions: 2 ,. a) F(S): 4s +9s+4 s(s+1)(s+2) 4sz+7s+3 b) F(s)=——2——— S(s+3) 2 c) F“): 4s +155+89 (s +1)(s2 + 4s + 29) ...
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Exam2F04 - ECE 232 fall 2004 Second Examination Dr. Glaser...

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