(Fall 1999)
A system has been partially modeled using a bond graph and characteristics as
shown.
a.
Annotate the diagram as needed.
Note that the capacitance is linear while the
resistance is nonlinear.
b.
Find the (nonlinear) state differential equations.
From the bond graph one finds,
( )
R
R
V
Q P
=
d
.
From the resistance characteristic
2
4
/10
R
R
Q
P
=  +
+
.
From the bond
graph and capacitance characteristic curve
0
0
/
25
R
P
P V C
P
V
=

=

.
Combining
( )
( )
0
2
4
/10
2
4
25
/10
R
R
R
V
Q P
P
P
V
=
=  +
+
=  +
+

d
.
Thus,
0
2
4
/10 2.5
V
P
V
=  +
+

d
.
c.
Determine the equilibrium state(s) of the system if
2
0
50N/m
P
=
.
Setting the time
changing variable to zero, gives
0
0
2
4
/10 2.5
P
V
=  +
+

.
Substitution and initial
Reduction, first gives
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This note was uploaded on 02/29/2008 for the course ME 242 taught by Professor Perreira during the Spring '08 term at Lehigh University .
 Spring '08
 Perreira

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