(Solved): Equations of motion. For the following rotational mechanical systems, draw a free-body diagram for ...

Equations of motion. For the following rotational mechanical systems, draw a free-body diagram for each inertia and find the equation(s) of motion for the angular position \( \theta(t) \) (or \( \theta_{1}(t), \theta_{2}(t) \), etc. if there are multiple inertias) as a function of the applied torque \( T_{a}(t) \). (a) 3 points. Figure 3: rot_two_inertias_wall (a) 3 points. Assume the pendulum rod is rigid and massless, and the angles \( \theta_{1} \) and \( \theta_{2} \) are small, so the spring remains approximately horizontal. Figure 4: pendulum2_spring