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I have a 07 f150 with 155000 km on it. I have an issue with the idle in that after it gets hot, 15/20 min into a drive, if I stop at a light and feather the gas to go forward, the motor starts running super rough….same at a drive through. The worst though is backing up….. as soon as I give it some gas and start to back up, the motor starts sounding like a diesel and the truck starts shaking. In both instances, if i give it a shot of gas, the idle sorts out and it runs fine.
I have gotten an oil change, 5-40 synthetic…I had all the spark plugs replaced (don't get me started on that debacle) and removed and cleaned the throttle body…. it was suggested that is might be a bad coil.
Are you getting any CEL indication? Anything this severe should have triggered a DTC by now I'm thinking.
It could be a bad COP, since you're recently changed (or had changed) the plugs something in that process could have been missed or done incorrectly. Bad plug, boot, wiring harness connector to the COP---all could contribute to your symptoms.
I've had something somewhat similar happen but it was triggered by cold weather; rough idle until operating temp, CEL on, smoothed right out until next cold morning.