The block diagram of a control system is shown in Fig. The transfer function $$G(s) = Y(s)/U(s)$$ of the system is

The loop gain $$GH$$ of a closed loop system is given by the following expression $${K \over {s\left( {s + 2} \right)\left( {s + 4} \right)}}.$$ The value of $$K$$ for which the system just becomes unstable is

A control system with certain excitation is governed by the following mathematical equation $$${{{d^2}x} \over {d{t^2}}} + {1 \over 2}{{dx} \over {dt}} + {1 \over {18}}x = 10 + 5{e^{ - 4t}} + 2{e^{ - 5t}}$$$
The natural time constants of the response of the system are

The simplified block diagram of a $$10$$-bit $$A/D$$ converter of dual slope integrator type is shown in Fig. The $$10$$-bit counter at the output is clocked by a $$1$$ $$MHz$$ clock. Assuming negligible timing overhead for the control logic, the maximum frequency of the analog signal that can be converted using this $$A/D$$ converter is approximately. Input sample to be converter