Determine a first-order ordinary differential equation to describe the rotating machine (consider viscous friction) as a dynamic system where the output is the angular velocity of the inertia J , , 2 w2 and the input is the motor torque, τ . Calculate the solution to this equation. Consider: τ = 1 N m, mm, mm, kg-m 2 /s, kg-m 2 /s, kg-m 2 r 5 , 1 = 2 r 00 2 = 5 b .01 1 = 0 b .1 2 = 0 J .0031 1 = 0 J 5 2 = 2 kg-m 2 . Plot the response of w (t) with three different initial conditions 2 w (0) 0, 3, 6 rad s