Example Results with the Symbolic Inverse Laplace Transform Applet

The following table contains some commonly encountered rational polynomial functions with known inverse Laplace transform results in the first two columns. The corresponding inputs of N(s) and D(s) are shown in the 3rd column, and the applet's output is in the last column. Note that straight simplifications have been done (primarily by removing the zero terms and multiply out the coefficients) with the outputs.

H(s)

h(t)

N(s)/D(s)

Applet Output

n=0,a=3: 1/(s+3)

n=1,a=2: 1/(s+2)(s+2)

n=2,a=1: 1/(s^3+3s^2+3s+1)

1.0*exp(-3.0*t)

1.0*t*exp(-2.0*t)

0.5*t^2*exp(-1.0*t)

a=2: 2/(s)(s+2)

-1.0*exp(-2.0*t)+1.0

a=1,b=2: 2/(s^2+2s+5)

2*(-sin(2.0*t)*(-0.5))*exp(-1.0*t)

a=1,b=2: (s+2)/(s^2+2s+5)

2*(cos(2.0*t)*(0.5)-exp(-1.0*t)

a=2: 2/(s^2-4)

-0.5*exp(-2.0*t)+0.5*exp(2.0*t)

a=2: s/(s^2-4)

0.5*exp(-2.0*t)+0.5*exp(2.0*t)

a=2,b=3: 1/(s+2)(s+3)

-1.0*exp(-3.0*t)+1.0*exp(-2.0*t)

a=2: (s^2-4)/(s^2+4)(s^2+4)

2*(cos(2.0*t)*(0.5*t))

a=2: 1/(s)(s^2+4)

2*(cos(2.0*t)*(-0.125))+0.25

a=2: 1/(s^2+4)(s^2+4)

2*(cos(2.0*t)*(-0.0625*t)-sin(2.0*t)*(-0.03125))

a=2: s/(s^2+4)(s^2+4)

2*(-sin(2.0*t)*(-0.125*t))

a=2: s^2/(s^2+4)(s^2+4)

2*(cos(2.0*t)*(0.25*t)-sin(2.0*t)*(-0.125))

a=2: 2/(s^2)(s+2)

0.5*exp(-2.0*t)+1.0*t-0.5

Copyright © 2000 - 2011 EE Circle Solutions. All rights reserved.