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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 sourcefree 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(tI) — (t3)u(t—3) + 2(t5)u(t5) e (t—6)u(t6) + 6(1)
for half credit. “’0 403 (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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This note was uploaded on 02/18/2010 for the course ECET 232 taught by Professor Gla during the Spring '07 term at NJIT.
 Spring '07
 Gla

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