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Have you checked the TSB list above? I doubt it's your drive shaft but I would recommend looking at the TSB's and seeing if the problem is listed. Here's the link: https://www.ford-trucks.com/tsb/tsb.php
The only thing I have ever had act like that was the housing that holds the cluster gear broke it only shook going up hill. However it could be a coil or fuel problem also.
Rezvani's Latest Post-Apocalyptic Monster Is a Ford F-150 Raptor Underneath
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