However there are some GE motors that have an external start relay. That relay also has normally closed contacts. Once running, a small current(actually a voltage sensitive relay) is generated in the start winding that causes the start relay to 'pick' and thus open the contacts. That generated voltage is greater than the voltage across the relay coil when motor is starting.
All this is more than you need to know for the task at hand. Wherever the contacts are located,(internal centrifugal switch or external start relay) they need to be checked to make sure they are closed 'at rest'. That is step one.
All this extra info lets you understand how it works when 'normal'.
Humming/growling is not normal.