01 Bonneville Shakes when accelerating and turning right

My 01 Bonneville shakes when 

pressing accelerator and when
making right hand turns.
You can feel it in the
steering wheel, especially during
right hand turns.
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Have the vehicle inspected.

If what you’re feeling is a worn ball joint/tie rod end, it can cause you to lose control of vehicle if it finely fails.

Tester