[richappy]

There are two causes of shaking in these washers, either a weak support spring or a transmission problem.
Both can be fixed by adding a helper spring to the existing rear support spring.
Pull outer cover off and locate the tub frame spring in the back.
Buy a GE dishwasher spring WD1X1354, about six inches long and add it to the existing spring. This will fix the problem. You might want to remove the old spring to prevent spring noise while spinning.