A control system is defined by the following mathematical relationship $$${{{d^2}x} \over {d{t^2}}} + 6{{dx} \over {dt}} + 5x = 12\left( {1 - {e^{ - 2t}}} \right)$$$

The response of the system as $$\,t \to \infty $$ is

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 following program is written for an $$8085$$ microprocessor to add two bytes located at memory addresses $$1FFE$$ and $$1FFF$$
$$\eqalign{ & LXI\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,H,\,\,\,1FFE \cr & MOV\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,B,\,\,\,M \cr & INR\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,L \cr & MOV\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,A,\,\,\,M \cr & ADD\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,B \cr & INR\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,L \cr & MOV\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,M,\,\,\,A \cr & XRA\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,A \cr} $$

On completion of the execution of the program, the result of additional is found.

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