Hi,
Go to this page:
http://www.mobilehomerepair.com/NordyneElec.html
Contactor # 621958 @ $17.00 each . Your furnace has two of these in the circuits to the heating elements
Relay N.O. #621898 (Cooling) @ $7.44
Relay N.C. # 621899 (Heating) @ $8.25
These two relays are in the circuits to the blower motor for heating and cooling modes.
All of these play into the circuits you mentioned and any one or more could cause the hum or be a part of this.
It would take understanding the wiring diagram and testing the circuits in action to know what is happening.
Any or all can be ordered from above page by adding to cart and ordering through PayPal or by calling toll free to 1-877-263-7860 after 9AM CST and charging to Visa or Mastercard.
If outside the U.S., let us know for added info.
From what you stated, I would suspect one or both Contactors for noise and 621899 relay for on/off/on/off of blower motor.
With that said, without total testing, I would replace all 4 as each can/will fail at some time due to contacts pitting from arcing when opening and closing often with calls for heat and cool.
Thanks.
Take care and best wishes,
Robert
Some people are Humbly Grateful, while some are Grumbly Hateful.................... Which one are you ?