Example 12.12.  Find the inverse Laplace transform  [Graphics:Images/LaplaceTransformMod_gr_192.gif].  

Explore Solution 12.12.

Enter the function F[s] and find its partial fraction expansion.

[Graphics:../Images/LaplaceTransformMod_gr_194.gif]





[Graphics:../Images/LaplaceTransformMod_gr_195.gif]



The transform F[s] is a linear combination.

[Graphics:../Images/LaplaceTransformMod_gr_196.gif]




[Graphics:../Images/LaplaceTransformMod_gr_197.gif]

 

 

 

 

The inverse of  [Graphics:../Images/LaplaceTransformMod_gr_198.gif]  and  the inverse of  [Graphics:../Images/LaplaceTransformMod_gr_199.gif].  
Hence  [Graphics:../Images/LaplaceTransformMod_gr_200.gif].

[Graphics:../Images/LaplaceTransformMod_gr_201.gif]





[Graphics:../Images/LaplaceTransformMod_gr_202.gif]



Aside. We can check this with Mathematica's  result using the LaplaceTransform package.

[Graphics:../Images/LaplaceTransformMod_gr_203.gif]




[Graphics:../Images/LaplaceTransformMod_gr_204.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) 2006 John H. Mathews, Russell W. Howell