2011 Mitsubishi Endeavor - Shakes

begins to shake when take off after it is driven a short distant

I would have the motor and tranny mounts checked.

Mitsubishi Endeavor: Shaking When Accelerating → Diagnosis | Drivetrain Resource (700r4transmissionhq.com)

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That’s the sort of problem that could be a safety hazard. Suggest to take your Endeavour to shop for inspection asap. If you decide to drive at all, slow speed driving only until the inspection results are in.