System Control Query - Find y(t) from Y(s)

[DrMath]

Dear PF Friends,

Given the system to be controlled.
I'm stuck in finding the inverse laplace (to find y(t) from Y(S)) - any advice?

 

[matematikawan]

Must forgive me if it not correct. I'm trying

$$Y(s)=\frac{1}{s} ( \frac{k}{s(s+1)+k}) = \frac{1}{s} ( \frac{k}{(s+1/2)^2+ (k-1/4)})$$

Invert
$$y(t)=\frac{k}{\sqrt{k-1/4}} \int_0^t e^{-t/2} \sin{(\sqrt{k-1/4})t } dt$$