Causes When Car Shakes When Accelerating But Not When Coasting

Here are the causes I have seen when a vehicle shakes when it is accelerating but not when coasting.
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A vibration that occurs only under acceleration is most likely a drivetrain issue, such as a bad CV axel or U-Joint.
Most Common Causes
CV Axel (Often Makes Ticking Noise)
Driveshaft U-Joint
Unbalanced Tire or Bad Rim
Loose Lug Nuts
Motor Mount
Transmission Mount
Less Common Causes
Engine Problem (usually with get code)
Transmission Problem (usually with get code)
Frame Damage
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