PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

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

dit

dt

it

dit

dt

it t

2

2

2

(^02)
1
00
()
()
()

()
for
dit
dt
it
2
2 144 0
()

()
FIGURE 2.94
Plots of numerical transient solutions of Example 2.27.
21.81.61.41.210.80.60.40.20
10
15
20
plots of: [vc(t), vr(t), and i(t)] versus t
21.81.61.41.210.80.60.40.20
5
0
10
21.81.61.41.21
time in sec
0.80.60.40.20
2
0
4
6
i(t) in volts
vr(t) in volts
vc(t) in volts