The print wheel control system of a word processor, is shown in Fig P9.7. The control system consists of a DC motor driving belts and pulleys. Assume that belts are rigid. \(\mathrm{T}_{m}(t)\) is motor torque, \(\theta_{m}(t)\) is motor displacement (angular), \(y(t)\) is linear displacement of print wheel, \(\mathrm{J}_{m}\) is motor inertia, \(\mathrm{B}_{m}\) is motor friction, \(r\) is the pulley radius and \(\mathrm{M}\) is the mass of print wheel.
(a) Write the differential equation describing system dynamics.
(b) Obtain transfer function model of system, \(\mathrm{Y}(s) / \mathrm{T}_{m}(s)\).

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T 771 Motor m B, 0 'm Print wheel M Pulley