If $$F\left(s\right)\;=\;\frac\omega{s^2\;+\;\omega^2}$$, then the value of $$\underset{t\rightarrow\infty}{\lim\;}f\left(t\right),\;\left\{where\;F\left(s\right)\;is\;the\;L\left[f\left(t\right)\right]\right\}$$

Consider a feedback control system with loop transfer function $$$G\left(s\right)H\left(s\right)=\frac{K\left(1+0.5s\right)}{s\left(1+s\right)\left(1+2s\right)}$$$ The type of the closed loop system is

If $$L\left(f\left(t\right)\right)=\frac{2\left(s+1\right)}{s^2+2s+5}$$ then f(0⁺) and f($$\infty$$) are given by [Note: 'L' stands for 'Laplace Transform of']

For a second order system, damping ratio $$\left(\xi\right)$$ , is 0 < $$\xi$$ < 1 ,then the roots of the characteristic polynomial are