My steering column just starting shaking and vibrating, while driving.

Hello, steering that shakes while driving is most often related to a bad tire, a bad wheel, or an out of balance wheel. You mentioned the fact you had the wheels rotated and balanced -- I would recommend taking the vehicle back to whoever did the work and explain to them what's going on. They should be able to recheck the balancing, road test the vehicle with you, and troubleshoot what's going on without much trouble. As a side note: if the vibration only occurs while braking, it could be a brake system issue. Good luck!

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