You asked:
I notice the spring just goes from each end of the rod. could this be the issue.
Not sure of your question here but here is some info that might help you.
This link is about how to adjust the governor SPRING sensitivity. You can search on-line and find more general info about such.
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What is the model number on the Honda gen?
How do you know it's running a 60 HZ when you hold the rod?
Do you have a HZ meter or going by feel?
Just couple basics here as Rivets says:
Not knowing your model number:
Normally on a generator the governor spring has constant tension and some Honda's have a big Phillips screwdriver adjust or similar and the tension is increase on the governor spring to increase the HZ and decreased tension to reduce HZ and several holes in the gov arm or linkage so as to adjust the sensitivity of the governor. (sensitivity is how long it takes for the governor to stop hunting up/down when a 80% load is applied and removed) 3000 x 80%=2400 watts or around 2000 watts. The 3500 watts is for intermittent surge loads only.
You can probably get a general idea of such by searching on-line on how to adjust a emergency gen governor for correct Hertz.
Also it's quite common for the governor springs to become weak and require replacement and on the Honda's sometimes a thread locker (blue or green) has to be applied to the governor adjust screw so as vib's does not loosen the adjustment screw/nut.
Unloaded you need about 63hz and 58 when a 80% RESISTANCE LOAD is applied. (average of 60hz)
Resistance load is electric heating elements or light bulbs, not motors.