PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

354 Practical MATLAB® Applications for Engineers

where y(t) = £−^1 [Y(s)]. The process of evaluating the coeffi cients A, B, and C by hand

is illustrated as follows:

A

ss

ss s s





()()

()( ) ()()

410

12

10

12

5

0

⋅



B

ss

ss s s





()()

()( )

410 1

12

6

 1



C

ss

ss s s





()()

()( )

410 2

12

1

 (^2)
then
Ys
ss s
()




56
1
1
2

and
y(t) = £−^1 [Y(s)] = 5u(t) − 6e−t u(t) + e−^2 t u(t)
R.4.99 Let us use the concepts developed by the Laplace technique, in the analysis of elec-
trical networks. Recall that vR(t) = R i(t) (Ohm’s law), and its Laplace transform is
given by £^ [vR(t)] = £[R ⋅ i(t)] = R £[i(t)], then
VR(s) = R * I(s)
Ohm’s law holds in the frequency domain, and the impedance Z(s) (Ω) is defi ned by
Zs
Vs
Is

()

()

()

The time–frequency domain relation for a pure resistor R is illustrated in Figure 4.9.

R R

Time domain s-domain

FIGURE 4.9
Time–frequency domain relation for R.