194
Practical MATLAB
® Applications for Engineers
Note that the analytical solution fully agrees with the symbolic and numerical solutions
shown in Figures 2.93 and 2.94.
Example 2.28
Steady-state conditions exist in the network shown in Figure 2.95 at t = 0
−
, when the
V 0 = 10 V source is connected to the RCL circuit. At t = 0
+
, the switch moves downward,
and the source V 0 = 10 V and resistor R are disconnected from the LC structure, where
it remains for t ≥ 0.
Write the second-order loop differential equation in terms of the current i(t), solve
and plot i(t) using MATLAB over the range 0 ≤ t ≤ 1 s, and verify that the LC network
is an ideal oscillator.
ANALYTICAL Solution
CL
or
CL
d i t
dt
i t
d i t
dt
i t
t
2
2
2
2
0
1
0
0
( )
( )
( )
( )
ϩ
ϭ
ϩ
ϭ
for ജ
d i t
dt
i t
2
2
144
0
( )
( )
ϩ
ϭ
FIGURE 2.94
Plots of numerical transient solutions of Example 2.27.
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
10
15
20
plots of: [vc(t), vr(t), and i(t)] versus t
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
5
0
10
2
1.8
1.6
1.4
1.2
1
time in sec
0.8
0.6
0.4
0.2
0
2
0
4
6
i(t) in volts
vr(t) in volts
vc(t) in volts
CRC_47760_CH002.indd 194
CRC_47760_CH002.indd 194
7/23/2008 1:38:59 PM
7/23/2008 1:38:59 PM