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ECE210  Fall 2010  Homework 06 (Due: Oct 06, 2010 at 5 p.m.)
1. Consider the
n
thorder homogeneous ODE in p. 114 of the textbook and its general solution in terms of the
characteristic polynomial.
(a) Solve the ODE by the phasor method (i.e. solve
d
n
y
dt
n
+
a
1
d
n

1
y
dt
n

1
+
···
+
a
n
y
(
t
) =
f
(
t
)
and ﬁnd the phasor
output
Y
as a response to a phasor input
F
, where
y
(
t
) =
Re
{
Y e
jωt
}
and
f
(
t
) =
Re
{
Fe
jωt
}
).
(b) Where does the characteristic polynomial appear in the output expression?
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Unformatted text preview: (c) Does the frequency of the output diﬀer from the frequency of the input? (d) Why doesn’t the term ( ωt ) appear in the phasor solution? 2. Textbook problem 4.1 3. Textbook problem 4.2 4. Textbook problem 4.3 5. Textbook problem 4.9 6. Textbook problem 4.10 7. Textbook problem 4.11 1...
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This note was uploaded on 03/05/2011 for the course ECE 210 taught by Professor Staff during the Fall '08 term at University of Illinois, Urbana Champaign.
 Fall '08
 Staff

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