The transfer function of a linear time invariant system is given as $$G\left( s \right) = {1 \over {{s^2} + 3s + 2}}$$

The steady state value of the output of the system for a unit impulse input applied at time instant $$t=1$$ will be

The transfer function of a system is given as $${{100} \over {{s^2} + 20s + 100}}.$$ The system is

$$R-L-C$$ circuit shown in figure

For a step input $${e_{i,}}$$ the overshoot in the output $${e_{0,}}$$ will be

Consider the feedback system shown below which is subjected to a unit step input. The system is stable and has following parameters $${k_p} = 4,\,\,{k_i} = 10,\,\,\omega = 500\,\,$$ and $$\xi $$ $$=0.7.$$ The steady state value of $$z$$ is