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Unformatted text preview: ECE 220 Exam #2
Spring 2007
Section 002 Student Name: LAST NAME
(PRINT) FIRST NAME
(PRINT) (SIGNATURE) By signing I am stating that I have taken this exam in accordance
with the NCSU honor code. Show all work  no credit for answer only PROBLEM 1 (20) Consider the differential equation and the initial conditions given below. d2v(t) + dv(t) dﬁ— d, +v<r>=2e3‘u<r> v<0>=2 W0): .. r“
a) Identify the type of damping. 11+ ﬁf l : O ”All; 111:3 ,7,
9— c.
U Adf’fcluM‘Sg Ci b) Find the complementary solution, v (I), for t 2 0. DO NOT SOLVE for constants. Your answer should not contain any complex terms. , __ f3 .67»
a9 1 m3 t: ~ 5% (Jim—5V6 H
a l. m ( {1‘9 e U
VEM— Ce: e, * + w “w “ﬂawed _. ,1 ' 02 ' 3 ”f ._ Cga"?(ed( t+9l+ a » )uH) _. L l: x: ..
: 2 C e, 1 ( K.) ‘1) K 35’& "V .9) M (1‘ )
c) Find the particular solution, vp (t) , for t 2 0. VPOf); A @‘3’tu (11) (Dual): %
€ﬁe’7'3??? 7L. AH) e}%f+)+ Adﬁ—ZH} .= 2 e“ um "‘v ’3 a 3 t
9"“ Hi; 3'.. 63 a”)
P 4.
d) In the system represented by the differential equation below, select a value for the parameter b so that the system is overdamped. d2v(t) +1) dv(t) dtz dt
b7._ 36> >0
b > 6 + 9v(t) = (8t)u (t) .f PROBLEM 2 (30) Consider the differential equation and the initial condition given below. Find the total solution for t 2 0. d2?) + 4v (t) = [6 + cos(4f)lu (t)
1
v(0) — E Useful identity: a cosa + b sina 2 Va 2 + [)2 cos(a — arctan %) 3 + ’
V; (Ti ):. C e 11 u ("H fl .1 {7+ "’2 A; 4"“ 3}?“ (‘i i z [(13% L1if i ' (ﬁt/((7')? 0 i' if A ("A {i i: I“) 5 i ‘2’
,4“! ('04:: ,2 EX» £05 (11%, + a) u (—f) (aw/:0)
— 4 {35: of 17% ﬁdﬂlféliviwg 3 MS 55/ J‘ ”l” ahalﬂ" S (n7 75) M (4)
.~' —— X“ .: '7 (["t
49313 (05i(4.4:.+9_.arc/m 77?) (“32> i)
[ii : ——;—:__, 9 : “I
1/3423, L/
i , rr ‘“ H)
y“ (4 2v;'_ (35(«14: / J)“
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will: PROBLEM 3 (20) a. Give the phasor representation of the sinusoidal signal below. I v (t) = sin(2m +545) + 2003(2m 115:) N ’3'? , rr
v a? , v '2
:2 2.87%.a....+.,: ,.
”t 2 3n, :2. Jr;
“W
l ’1.  a /
z E 1" {3: , 5 7
b. Consider the complex valued function, H (w) = j10
10+ja) Let this H ((0) represent the relationship between the phasors of the input signal and the output signal of a
circuit in the following form. {/4 (w) =H(w).1}s (cu) Find the output signal v0 (t) , when the input signal is vs (I) =10sin(10t +Jr/ 4) ﬂ/Z
'3 \0 .. :l  5 3
_ mum«MW ~~ W4: * ~, 11/
H {10) r W45“) ‘“‘3 \TZ'”) ?
W
ll: ~«w...
N 6‘3L AD 63 7 2: ‘0
0(i0) :“ Mw—wf—ew‘ “i ’7:
C: C 3 7 “Z PROBLEM 4 (15) Consider the differential equation and the initial condition given below. dv(t) + 2th (t) 2 (31‘ + 3)u (t)
dt
v(0)=3
tvvxt ’ 'ch
‘ t \ J ’ I
a) IdentifythetypeofDE: Nan “Maven! V&(\/I/\C® (0 ﬂ /1 old? f b) Determine the values of the solution v(t) for t = [0, 0.1,0.2] using Euler’s method with a step size of
h = 0.1 sec. Wt “0:110 .3  2—3 V W 3 (at + a) u H)
in 3mm : ~2 1333%; + M333'3‘m) 36+) 7/,[0l2l
Vmu); 0+ Oll3 + 7(0’2w; .3: _. la O/i ’ ’ Mr” PROBLEM 5 (15) The driving force and the particular solution pair given below corresponds to a first order system. Give a
differential equation representation of this system. vs (t) = cos(10t)u(t)
1
v” (I) _ 10¢? cos(10t—%)u(t) TC"
(/UJ, Sin (10%»5) + 01 fl; “3‘5 (mi? ”3;; : (05 “0‘9
__/ / VE— ? 0‘“ 2,. /(§ ; V
/l Ewell?» ,L +3—3i
i\\:+§i© 1 if)
a Z;
262 423» ...
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 Summer '08
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