Answer to Question #256600 in Electrical Engineering for Abubakar Tanveer

Question

Find inverse Laplace transform of:

G(s)= S / (S+1) (S+1+j1)^2 (S+1-j1)^2

Solve step by step and briefly.

Answer 1

$L^{-1}\left\{\frac{s}{s^2+4s+5}\right\}\\ =L^{-1}\left\{\frac{s+2}{\left(s+2\right)^2+1}-2\cdot \frac{1}{\left(s+2\right)^2+1}\right\}\\ Use\:the\:linearity\:property\:of\:Inverse\:Laplace\:Transform\\ \mathrm{For\:functions\:}f\left(s\right),\:g\left(s\right)\mathrm{\:and\:constants\:}a,\:b:\quad L^{-1}\left\{a\cdot f\left(s\right)+b\cdot g\left(s\right)\right\}=a\cdot L^{-1}\left\{f\left(s\right)\right\}+b\cdot L^{-1}\left\{g\left(s\right)\right\}\\ =e^{-2t}\cos \left(t\right)-2e^{-2t}\sin \left(t\right)$