Page 96 - MATLAB an introduction with applications

MATLAB Basics ——— 81

p =
1.0e + 006*
4.6406
1.4250
0.3029
0.0336
0.0027
0.0001
0.0000
0
k = [ ]

Example E1.35: Determine the inverse Laplace transform of the following functions using MATLAB.
s 1
() =
(a) Fs (b) Fs
() =
( ss + 2)(s + 6) ss 5)
( +
2
3s + 1 s − 25
() =
() =
(c) Fs (d) Fs
2
2
(s + 2s + 9) ( ss + 3s + 20)
Solution:
(a) >> syms s
>> f = s/(s*((s + 2)*(s + 6)));
>> ilaplace( f )
ans =
1/2*exp(–4*t)*sinh(2*t)
(b) >> syms s
>> f = 1/((s^2)*(s + 5));
>> ilaplace(f )
ans =
1/3*t – 2/9*exp(–3/2*t)*sinh(3/2*t)
(c) >>syms s
>> f = (3*s + 1)/(s^2 + 2*s + 9);
>> ilaplace( f )
ans =
3*exp(–t)*cos(2*2^(1/2)*t)–1/2*2^(1/2)*exp(–t)*sin(2*2^(1/2)*t)
(d) >>syms s
>> f = (s –25)/(s*(s^2 + 3*s +25));
>> ilaplace( f )
ans =
5/4*exp(–3/2*t)*cos(1/2*71^(1/2)*t)+23/284*71^(1/2)*exp
(–3/2*t)*sin(1/2*71^(1/2)*t)–5/4
Example E1.36: Find the inverse Laplace transform of the following function using MATLAB.

(s 2 + 9 +s 7)( +s 7)
() =
Gs
( + 2)( + 3)(s 2 + 12 + 150)
s
s
s

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