Problem 1: The figure below shows a motor (characterized by an inertia J1 and a rotational damping b,1)driving a flywheel with a bearing (characterized by a second inertia J2 and

a rotational damping b,2) through aset of gears with radii R, and R2. The input is a motor torque m(t). The coordinates are defined as shown in thefigure. Assume the shafts are rigid. (a) (10 Points) Determine the equations of motion in terms of the input/motor side variables min (t), 0, (t),and its derivatives. [] \ddot{\theta}_{1}+[] \dot{\theta}_{1}+[] \theta_{1}=M_{i n}(t) = 0.05 kg-m², R1b) (5 Points) Suppose J1the second inertia such that the total inertia (actual plus reflected) seen on the motor/input side is less orequal 0.17 kg-m².= 0.05 m and R2= 0.25 m, calculate the maximum value for = 1.2 N-s-m and b, 2(c) (5 Points) Given the values from part (b) and b,1following represents the response to a step input moment m(t) = 30 u(t) N-m. Quantitatively justifyyour answer for full credit.20 N-s-m, which of the