Mixing synthetic and conventional oils is not a problem as they're compatible with each other. If the car is shaking, get it checked out by a mechanic. Com/faqs/motor-oil/full-synthetic-motor-oil.
I have seen it cause problems. The synthetic oil is fantastic if you start using it at an early mileage, Below 75,000 but it's really slick and has a better lubricity than conventional oil. So what happens is that a vehicle that has over 100,000 miles and has always used conventional oil "not synthetic" will often times leak in areas or an area such as the valve cover gaskets.
I've personally seen it happen and it is a more common occurrence than what you will ever hear of because most people usually don't relate the leak with changing to a different oil.
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