Join Date: Feb 2013
Location: New York
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Typically the throttle cable would directly control the opening and closing of the throttle plate. A spring to the throttle shaft would usually be for the governor to control the maximum speed of the engine. You need to have someone throttle it up and down and watch what the throttle actually does. It's possible that the cable to the throttle just isn't doing its job.
If you could find the model number of the Briggs engine on your mower, which is often on shrouding near a cylinder head or on a tag on the engine, that would help find more detailed diagrams.