Question

2p+3/p²+2p+3 by using first shifting theorem of inverse Laplace transform

Answer 1

Answer:

Step-by-step explanation:

Let F(p) = $\frac{2p+3}{p^2+2p+3}$

$=\frac{(2p+2)+1}{(p+1)^2+1} \\F(p)=\frac{2(p+1)}{(p+1)^2+2} +\frac{1}{(p+1)^2+2}$

Taking inverse Laplace transform we get

f(t) = $2e^{-t}\cos \left(\sqrt{2}t\right)+e^{-t}\frac{1}{\sqrt{2}}\sin \left(\sqrt{2}t\right)$