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

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

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

The system shown in the figure is

If the loop gain $$K$$ of a negative feedback system having a loop transfer function $$K\left( {s + 3} \right)/{\left( {s + 8} \right)^2}$$ is to be adjusted to induce a sustained oscillation then