Q3) (10 points). Consider a geared DC motor with an inertial and friction load. a) Use a numerical method to predict and plot the velocity, and current as a function of time when the throttle is set to 12V for 1 seconds, then - 12V for 1 second, then set to 0. Include winding inductance in your equation of motion. The following parameters refer to the speed and torque and friction at the output of the gearbox Total system inertia: 1.0x10-3 kgm2 Motor Torque constant (KT) 0.3 Nm/A Motor Electrical constant (K) 80 rpm/V Motor Terminal resistance (R) 2.0 Ohm Winding inductance (L) 8.0 mH Motor break away friction 400 gem Motor dynamic friction 200 gcm b) The motor driver has a steady state current limit of 2 A. Does the current exceed this limit, and for how long? Q3) (10 points). Consider a geared DC motor with an inertial and friction load. a) Use a numerical method to predict and plot the velocity, and current as a function of time when the throttle is set to 12V for 1 seconds, then - 12V for 1 second, then set to 0. Include winding inductance in your equation of motion. The following parameters refer to the speed and torque and friction at the output of the gearbox Total system inertia: 1.0x10-3 kgm2 Motor Torque constant (KT) 0.3 Nm/A Motor Electrical constant (K) 80 rpm/V Motor Terminal resistance (R) 2.0 Ohm Winding inductance (L) 8.0 mH Motor break away friction 400 gem Motor dynamic friction 200 gcm b) The motor driver has a steady state current limit of 2 A. Does the current exceed this limit, and for how long