Determine the transient response

Question

How do i Determine the transient response of an transfer function if it's in the s domain?? the obvious answer would be using inverse laplace transform, but how come??

consider i have system like this $\frac{2+1}{s(s+1)^2}$

Answer 1

Hints: You search for the partial fraction decomposition of the given expression as in writing it as $A/s +B/(s+1) + C/(s+1)^2$, and find $A,B,C$. Then the inverse Laplace transform of $ K/(s+a)^n$ is $Ke^{-at}t^{n-1}/(n-1)!$. Then you add the contributions from each of the three terms.