In the system whose signal flow graph is shown in the figure, $${{U_1}\left( s \right)}$$ and $${{U_2}\left( s \right)}$$ are inputs. The transfer function $${{Y\left( s \right)} \over {{U_1}\left( s \right)}}\,$$ is

A closed loop system has the characteristic equation given by
$${s^3} + K{s^2} + \left( {K + 2} \right)s + 3 = 0.$$ For this system to be stable, which one of the following conditions should be satisfied?

The transfer function of a system is given by $${{{V_0}\left( s \right)} \over {{V_i}\left( s \right)}} = {{1 - s} \over {1 + s}}$$

Let the output of the system be $${v_0}\left( t \right) = {v_m}\sin \left( {\omega t + \phi } \right)$$ for the input $${v_i}\left( t \right) = {v_m}\sin \left( {\omega t} \right).$$ Then the minimum and maximum values of ϕ (in radians) are respectively

Consider the unity feedback control system shown. The value of $$K$$ that results in a phase margin of the system to be $${30^0}$$ is ____________. (Give the answer up to two decimal places).