There is no way a motor is well-modeled by a capacitor, either analytically or intuitively. It's a coil of wire, practically a poster child for an inductor.
This does have lumped resistance elements, but by the time you put the two inductors and two resistors in to the differential equation with forcing
sin (2*pi*60*t) u(t),
you're not going to be in a good place as far as intuition goes.
In fact, overall, I'm not seeing much intuitive sense in your summary. Once you really delve in to it, the subject of starting electric motors (AC and DC) is very complex.
Here's a motor's equivalent circuit from Wiki:
http://en.wikipedia.org/wiki/Induction_motor#Equivalent_circ...
This does have lumped resistance elements, but by the time you put the two inductors and two resistors in to the differential equation with forcing
you're not going to be in a good place as far as intuition goes.In fact, overall, I'm not seeing much intuitive sense in your summary. Once you really delve in to it, the subject of starting electric motors (AC and DC) is very complex.