A permanent magnet DC motor is coupled to a load through a gearbox. If the polar moments of inertia of the rotor and load are J
r and J
b, the gearbox has a N:M reduction (where N > M ) from the motor to the load, the motor has a starting torque T
s and a no-load speed max , and the load torque is proportional to its speed ( T
t = kω),
a. What is the maximum acceleration that the motor can produce in the load?
b. What is the steady state speed of the motor and the load?
c. How long will it take for the system to reach 95% of its steady state speed?