Figure $2$ shows a lifting apparatus comprising two pulleys connected by a flexible rope. A force f$($t$)$ applied to a handle of length L that is rigidly attached to Pulley $1$ raises $($and if the direction of the force is reversed lowers$)$ the suspended mass m$.$ The displacement of mis measured by the variable y$($t$).$ The two pulleys are constrained to rotate about their centers on bearings. Pulley $1($including the handle$)$ has an inertia $/$ about its center of rotation. Its radius is r and its bearing exhibits viscous damping b$.$ Similarly, Pulley $2$ has an inertia $/,$ a radius ry$,$ and its bearing exhibits viscous damping b$.$ The section of rope between Pulley $1$ and Pulley $2$ has stiffness K$,$ and that between Pulley $2$ and the mass m has stiffness K$.,$ The rope has zero mass. Determine the transfer function Y$($s$)/$F$($s$).$