The root-locus plot of a closed-loop system with unity negative feedback and transfer function KG(s) in the forward path is shown in the figure. Note that K is varied from 0 to $$\infty$$.

Select the transfer function G(s) that results in the root-locus plot of the closed-loop system as shown in the figure.

Consider an even polynomial p(s) given by

$$p(s) = {s^4} + 5{s^2} + 4 + K$$

where K is an unknown real parameter. The complete range of K for which p(s) has all its roots on the imaginary axis is __________.

Two linear time-invariant systems with transfer functions

$${G_1}(s) = {{10} \over {{s^2} + s + 1}}$$ and $${G_2}(s) = {{10} \over {{s^2} + s\sqrt {10} + 10}}$$

have unit step responses y₁(t) and y₂(t), respectively. Which of the following statements is/are true?

The block diagram of a closed-loop control system is shown in the figure. R(s), Y(s), and D(s) are the Laplace transforms of the time-domain signals r(t), y(t), and d(t), respectively. Let the error signal be defined as e(t) = r(t) $$-$$ y(t). Assuming the reference input r(t) = 0 for all t, the steady-state error e($$\infty$$), due to a unit step disturbance d(t), is __________ (rounded off to two decimal places).