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SOFTWARE FOR SOLVING LAPLACE TRANSFORMS We will use Sympy package in Python Instead EXAMPLE 3.9 Use the ilaplace Command in the MATLAB Symbolic Math Toolbox to find the inverse Laplace transform of a function: $Y(s) = \frac{s+2}{s^2+s+1}$ (3-98) Note that the roots of the denominator are a complex con- jugate pair, $r_1, r_2 = -0.5 \pm \frac{\sqrt{3}}{2}$. SOLUTION Enter the commands in the Command Window: sym s ilaplace ((s+ 2)/(s^2 + s + 1)) The MATLAB solution for y(t) is displayed as ans = exp(-t/2)* (cos ((3^ (1/2)t)/2) + 3^(1/2)sin((3^(1/2)*t)/2 This solution can be verified by comparison with the deriva- tion in Appendix L.

          SOFTWARE FOR SOLVING
LAPLACE TRANSFORMS
We will use Sympy package in Python Instead
EXAMPLE 3.9
Use the ilaplace Command in the MATLAB Symbolic
Math Toolbox to find the inverse Laplace transform of a
function:
$Y(s) = \frac{s+2}{s^2+s+1}$ (3-98)
Note that the roots of the denominator are a complex con-
jugate pair, $r_1, r_2 = -0.5 \pm \frac{\sqrt{3}}{2}$.
SOLUTION
Enter the commands in the Command Window:
sym s
ilaplace ((s+ 2)/(s^2 + s + 1))
The MATLAB solution for y(t) is displayed as
ans = exp(-t/2)* (cos ((3^ (1/2)*t)/2)
+ 3^(1/2)*sin((3^(1/2)*t)/2
This solution can be verified by comparison with the deriva-
tion in Appendix L.

SOFTWARE FOR SOLVING
LAPLACE TRANSFORMS
We will use Sympy package in Python Instead
EXAMPLE 3.9
Use the ilaplace Command in the MATLAB Symbolic
Math Toolbox to find the inverse Laplace transform of a
function:
Y(s) = (s+2)/(s^2+s+1) (3-98)
Note that the roots of the denominator are a complex con-
jugate pair, r1, r2 = -0.5 ±(√(3))/(2).
SOLUTION
Enter the commands in the Command Window:
sym s
ilaplace ((s+ 2)/(s^2 + s + 1))
The MATLAB solution for y(t) is displayed as
ans = exp(-t/2)* (cos ((3^ (1/2)*t)/2)
+ 3^(1/2)*sin((3^(1/2)*t)/2
This solution can be verified by comparison with the deriva-
tion in Appendix L.

Added by Patrick H.

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