Shake the vechicle
yes, 65;
yes
Is the car running ok? If yes and its only the vibration that's an issue most likely cause is motor mount(s)
Cylinder miss, broken motor mount, or vacuum leak.
Engine miss or rough idle, or broken motor mount
If other things vibrate as well as the steering wheel you might have a damaged motor/transmission mount.
check motor mounts
Only when accelerating, I would suspect a broken motor mount or bad CV joint.
rubber bushings in motor mount worn
A loose engine mount would not normally cause the engine to fall out because each car has several motor mounts. A loose mount could cause the motor to be off of balance.
loose motor mount(s), tire out of balance, bent wheel, driveshaft bent, or CV joins worn.