You have a motor that is powered by 24 VDC.  It free-runs at 600 radians/second, and stalls with a load of 125 in-lbs.  The time constant (τ) of the motor itself is 1.5 seconds.  The motor is connected through a set of 2 gears to a load having a torque of 300 in-lbs, an inertia of 2.5, and a friction of 0.5. 

The input gear (connected to the motor shaft) is 3 inches in diameter.  The output gear (connected to the load) is 12 inches in diameter.  From the information given, do the following:

a) Draw the diagram of the system.  Show all components (motor, gears, load) and indicate all individual values for torque, inertia, friction and the motor constant.

b) Draw the diagram representing the load parameters reflected back to the motor. Also show the time constant for this combined system.

c) Generate the torque-speed curve for the system.  (Hint: Remember that the speed is for the motor , not the load.)

d) The system is initially at rest.  Generate the speed vs. time curve for the system.  Also determine the load speed and plot it on the same set of axes as the system curve. (Hint: Remember that the system speed is for the motor, not the load.)