Multiply the entire equation by $R$ to clear the denominator: $$ J \ddotx = R T(t) - b_r \dotx - R^2 (m \ddotx + b \dotx + k x) $$
Comparing the 5th edition solution manual with its predecessors (notably the 3rd and 4th editions) reveals a shift in focus. Earlier editions focused more heavily on manual sketching of Nyquist plots and Nichols charts. The 5th edition solutions acknowledge the ubiquity of computer-aided design (CAD) tools. While this modernizes the curriculum, it risks atrophying the intuitive understanding of system behavior that comes from manual sketching. The manual attempts to balance this by explaining the logic behind the MATLAB outputs, rather than treating the software as a "black box." solucionario ingenieria de control moderna ogata 5 edicion
The equation of motion is: $$ J \ddot\theta = T(t) - b_r \dot\theta - R F \quad \dots \text(1) $$ Multiply the entire equation by $R$ to clear