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ME 375
Homework 5 : Solution
February 18, 2009
Problem 1
v
(3)
(
t
) + 4¨
v
(
t
) + 3˙
v
(
t
) =
f
(
t
)
Part A
Determine the transfer function V(s) to F(s)
Solution:
[
s
3
V
(
s
)

s
2
v
(0)

s
˙
v
(0)

¨
v
(0)]+4[
s
2
V
(
s
)

sv
(0)

˙
v
(0)]+3[
sV
(
s
)

v
(0)] =
F
(
s
)
[
s
3
+ 4
s
2
+ 3
s
]
V
(
s
)

[(
s
2
+ 4
s
+ 3)
v
(0) + (
s
+ 4)˙
v
(0) + ¨
v
(0)] =
F
(
s
)
The initial conditions are considered to be zero. The transfer function is :
V
(
s
)
F
(
s
)
=
1
s
3
+ 4
s
2
+ 3
s
Part B
We need to determine the free response:
Given:
f
(
t
) = 0
v
(0) = 1
˙
v
(0) =

1
¨
v
(0) = 2
V
(
s
) =
(
s
2
+ 4
s
+ 3)
v
(0) + (
s
+ 4)˙
v
(0) + ¨
v
(0)
s
3
+ 4
s
2
+ 3
s
1
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View Full Document V
(
s
) =
(
s
2
+ 4
s
+ 3)(1) + (
s
+ 4)(

1) + 2
s
3
+ 4
s
2
+ 3
s
Solution :
V
(
s
) =
s
2
+ 3
s
+ 1
s
3
+ 4
s
2
+ 3
s
Part C
What are the similarities between Part A and Part B?
They both have the same denominator.
Part D
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This note was uploaded on 08/28/2010 for the course ME 375 taught by Professor Meckle during the Spring '10 term at Purdue University.
 Spring '10
 Meckle

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