The damping ratio and undamped natural frequency of a closed loop system as shown in the figure, are denoted as $$\xi$$ and $$\omega$$_n are

Consider a closed loop system as shown.

$$ G_p(s)=\frac{14.4}{s(1+0.1 s)} $$

is the plant transfer function and $G_c(s)=1$ is the compensator. For a unit-step input, the output response has damped oscillations. The damped natural frequency is $\_\_\_\_$ $\mathrm{rad} / \mathrm{s}$. (Round off to 2 decimal places).

The unit step response of a system with the transfer function $$G\left( s \right) = {{1 - 2s} \over {1 + s}}$$ is given by which one of the following waveforms?

The open-loop transfer function of a $$dc$$ motor is given as $${{\omega \left( s \right)} \over {{V_a}\left( s \right)}} = {{10} \over {1 + 10s}}.$$ When connected in feedback as shown below, the approximate value of $${K_a}$$ that will reduce the time constant of the closed loop system by one hundred times as compared to that of the open-loop system is