Question #343132

Inverse Laplace Transforms

Find L^-1 {F(s)} when F(s) is given by


1. s+5/(s+1)(s-3)


1
Expert's answer
2022-05-25T17:10:46-0400

1.


s+5(s+1)(s3)=As+1+Bs3\dfrac{s+5}{(s+1)(s-3)}=\dfrac{A}{s+1}+\dfrac{B}{s-3}



=As3A+Bs+B(s+1)(s3)=\dfrac{As-3A+Bs+B}{(s+1)(s-3)}


A+B=1A+B=13A+B=5-3A+B=5




A=1,B=2A=-1, B=2




L1(s+5(s+1)(s3))=L1(1s+1)L^{-1}(\dfrac{s+5}{(s+1)(s-3)})=-L^{-1}(\dfrac{1}{s+1})




+2L1(1s3)=et+2e3t+2L^{-1}(\dfrac{1}{s-3})=-e^{-t}+2e^{3t}

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS