In Figure $1,$ a block with mass $\backslash ($ M$\_\{$L$\}\backslash )$ which is hanged from a ceiling with a spring with spring constant $\backslash ($ K$\_\{$L$\}\backslash )$ is driven in vertical direction with a fixed field direct current motor via a pinion gear that converts rotational motion to translational motion. The radius of the block that constitutes the rotational part of the pinion gear is given as $\backslash ($ r$\_\{$d$\}=$z$\_\{1\}\backslash )$ meters. The input of the system is input voltage of the direct current motor $\backslash ($ E$\_\{$a$\}($s$)\backslash )$ and the output is the vertical displacement of the block $\backslash ($ X$($s$)\backslash ).$ Sketch a detailed block diagram of the system and demonstrate all your required operations in detail.