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View Full Document Find v(t) for t>0
Hint: follow the steps:
(a)
For t>0, find the Thevenin equivalent circuit seen from port a and b.
(b)
For t>0, find the characteristic equation, and natural frequencies s
1
, s
2
.
(c)
Is this an overdamped, critically damped, or underdamped case?
(d)
Find the transient response v
t
(t) from initial values.
(e)
Find the steadystate response v
ss
(t).
(f)
Find v(t).
Solution
(a)
For t>0, find the Thevenin equivalent circuit seen from port a and b.
R
TH
=6Ω
V
TH
=4V
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View Full Document (b)
For t>0, find the characteristic equation, and natural frequencies s
1
, s
2
.
s
2
+
R
L
s +
1
LC
= 0
s
2
+
6
1
s +
1
0.2
= 0
°
1
=
−
1,
°
2
=
−
5
(c)
Is this an overdamped, critically damped, or underdamped case?
Overdamped
(d)
Find the transient response v
t
(t) from initial values.
In overdamped condition,
v
t
(t) = A
1
e
s
1
t
+ A
2
e
s
2
t
Finding
v
t
(0)
:
v
0
±
= v
t
0
±
+ v
ss
0
±
= 25V
−
4V = 21V
dv(0)
dt
=
dv
t
(0)
dt
+
dv
ss
(0)
dt
= 0
v
ss
t
±
=
−
4V
So
v
t
0
±
= A
1
+ A
2
= 25
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This note was uploaded on 05/19/2011 for the course BME 311 taught by Professor Zhang during the Spring '08 term at University of Texas at Austin.
 Spring '08
 Zhang

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