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AE 383 System Dynamics
Homework #4
Due: December 6, 2004
1.
Linearize the following nonlinear ordinary differential equation around the
equilibrium defined by
() 1
ft
=
:
3
27
( )
yy
y f
t
++
=
±±
±
.
2.
Following nonlinear ordinary differential equation is given:
q
h
h
+
−
=
2
/
3
±
, where
q
is
the input and
h
is the output.
The system is in equilibrium for
1
,
1
=
=
e
e
h
q
.
a.
Linearize this system for the equilibrium given.
b.
Find an approximate solution to the equations if
2
.
1
=
q
.
(Hint: use Laplace
transformation techniques).
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 Spring '11
 Melin

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