Q$5($a$)($i$)$ Draw analog simulation diagram for the following system.

$x^{}+8x^{}+25x=500,x(0)=40,x^{}(0)=150$

with, $|x{|}_{\text{m}\text{a}\text{x}}=50,|x^{}{|}_{\text{m}\text{a}\text{x}}=250.$

$($ii$)$ Obtain magnitude$-$scaled analog simulation of the system to utilize the full amplifier range of $0$ to $+10$ volts without any overloading.