Continuous rolling mill Consider continuous rolling mill depicted in above figure. Suppose that the motion of the adjustable roller has a damping coefficient b $,$ and that the force exerted by the rolled material on the adjustable roller is proportional to the material's change in thickness Fs$=$c$($T$-$x$).$ Suppose further that the DC motor has torque constant Kt and

a back emf constant Ke and that the rack$-$and$-$pinion has an effective radius of R $.$

$1)$ Without neglecting the effect gravity on the adjustable roller, draw a block diagram of the system that explicitly shows the following quantities Vs$($s$),$Ia$($s$),$Fm$($s$)($the force the motor exerts on the adjustable roller $)$ and X$($s$).$