A polynomial $$f\left(x\right)\;=\;a_4x^4\;+\;a_3x^3\;+\;a_2x^2\;+\;a_1x\;-\;a_0$$ with all coefficients positive has

The open-loop transfer function of a dc motor is given as $$\;\frac{\omega\left(s\right)}{V_a\left(s\right)}=\frac{10}{1+10s}$$, 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

The Bode plot of a transfer function G (s) is shown in the figure below. The gain (20 log $$\left| {G(s)} \right|$$ ) is 32 dB and -8dB at 1rad/s and 10rad/s respectively. The phase is negative for all $$\omega .$$ Then G(s) is

The state diagram of a system is shown below. A system is shown below. A system is described by the state variable equations

The state-variable equations of the system shown in the figure above are