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MAE107 Homework #1
Prof. M’Closkey
Due Date
The homework is due by 5PM, Thursday, January 15, 2009 to Mr. David Shatto in the 38137 foyer
(3rd ﬂoor Engineering 4).
Mandatory Reading
Please read the following sections from the course text:
1. All of Chapter 1. This introductory chapter broadly discusses dynamic analysis, block dia
grams and linear diFerential equations.
2. The introduction to Chapter 2 and the following subsections: 2.1 (don’t worry about the
author’s description of
through
and
across
variables); 2.6 (the ±rst physical system studied in
the lab is an RC circuit so this section provides a good review of modeling such systems).
3. The introduction to “Part B” starting on page 179.
4. The introduction to Chapter 6 and the following subsections: 6.1 through 6.7 (reviews linear,
±rstorder diFerential equations).
Problem 1
Recall the two RC circuit con±gurations:
1.
Lowpass flter
con±guration:
R
1
C
1
+
V
in
−
+
V
out
−
The diFerential equation relating the dependent variable
V
out
to the imposed voltage
V
in
is
given by
d
dt
(
V
out
(
t
)) +
1
R
1
C
1
V
out
(
t
)=
1
R
1
C
1
V
in
(
t
)
,
(1)
The reason this circuit and its associated diFerential equation is referred to as a lowpass
±lter will become clear when we discuss
Frequency response Functions
in several weeks.
1
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Highpass flter
confguration:
C
2
R
2
+
V
in
−
+
V
out
−
The diFerential equation relating the dependent variable
V
out
to the imposed voltage
V
in
is
given by
R
2
C
2
d
dt
(
V
out
(
t
)) +
V
out
(
t
)=
R
2
C
2
d
dt
(
V
in
(
t
))
.
(2)
The reason this circuit and its associated diFerential equation is re±erred to as a highpass
flter will become clear in several weeks.
²or this problem derive the relationship between the dependent variable
V
out
and the imposed
voltage
V
in
when these two circuits are connected together to ±orm a single as shown circuit:
R
1
C
1
C
2
R
2
+
V
in
−
+
V
out
−
In other words, the “
V
out
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 Winter '06
 TSAO

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