I checked with my HVAC service person, and he assured me that the damping grommets were in place and that the new motor was identical to the original. However, I found out that leaving the fan on ON rather than AUTO solved the problem, at least for now. With this information, I called technical support from TRANE, and was advised that the problem was probably in the fan (squirrel-cage) or its mounting; that it was getting slightly out of line when starting or stopping. My HVAC service man will pull and replace the fan next month (between the busy cooling and heating seasons) and we home this will be a permanent solution.
Thank you for your interest.
Sheldon