Question #343134

Inverse Laplace Transforms

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


4. s+7/s^2+2s+5


1
Expert's answer
2022-05-26T17:15:06-0400

4.


s+7s2+2s+5=s+1+6(s+1)2+4\dfrac{s+7}{s^2+2s+5}=\dfrac{s+1+6}{(s+1)^2+4}




=s+1(s+1)2+22+61(s+1)2+22=\dfrac{s+1}{(s+1)^2+2^2}+6\dfrac{1}{(s+1)^2+2^2}




L1(s+7s2+2s+5)=L1(s+1(s+1)2+22)L^{-1}(\dfrac{s+7}{s^2+2s+5})=L^{-1}(\dfrac{s+1}{(s+1)^2+2^2})




+6L1(1(s+1)2+22)=etcos(2t)+62etsin(2t)+6L^{-1}(\dfrac{1}{(s+1)^2+2^2})=e^{-t}\cos(2t)+\dfrac{6}{2}e^{-t}\sin (2t)




=etcos(2t)+3etsin(2t)=e^{-t}\cos(2t)+3e^{-t}\sin (2t)


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