Driveline issues: Worn or damaged driveline components, such as the driveshaft, universal joints, or transmission mount, can cause the car to vibrate or rock back and forth. Check for any signs of wear or damage to these components and replace them if necessary.
Engine issues: A misfire or other engine problem can cause the car to vibrate or rock back and forth. Check the engine for any trouble codes and diagnose and repair the underlying issue.
Suspension issues: Worn or damaged suspension components, such as the shocks, struts, or control arms, can cause the car to vibrate or rock back and forth. Check for any signs of wear or damage to these components and replace them if necessary.
Tire issues: Uneven tire wear or a damaged tire can also cause the car to vibrate or rock back and forth. Check the tires for any signs of wear or damage and replace them if necessary.
Wheel alignment: Incorrect wheel alignment can also cause the car to vibrate or rock back and forth. Have the car's wheel alignment checked and adjusted if necessary.
If you are unable to identify and resolve the issue on your own, it is recommended to take the car to a qualified mechanic for further diagnosis and repair.