Consider the math. An imbalance of one ounce (the weight of a rod bolt) 1” away from center at 2,000 rpm will be subjecting a force of 7 pounds. At 4,000 rpm, the force grows to 23.5 pounds. Double the speed again to 8,000 rpm and the force becomes 114 pounds! Keep in mind this is only with an imbalance of 1” away from the center of rotation. This is a great example to show why balance issues are negligible at low rpm but insanely important at high rpm.
The 3800 has 6 cylinders with two banks of 3, 90 degrees apart (90 degree V6 engine). This engine is actually 2 inline 3 cylinder engines together. At any given time a cylinder on the front is in the same position as a cylinder in the rear. The crank shaft has 30 degrees offsets for journals where rods are next to each other. These 30 degrees, plus the 90 degree V gives you 120 degrees. 3 cylinders by 120 degrees results in 360 degrees or a full circle.
This design has some inherent issues though. As the 3 cylinders on one bank move up and down, a shock is generated as they change direction (at the top and bottom of stroke). This shock cannot be countered by the other bank because they are on a 90 degree plane from each other. This creates an annoying harmonic that doesn’t affect engine balance or performance but is noticeable in the car. As the engine speed rises, so does the frequency of this shock and it’s not felt much as it’s absorbed through the mounts and chassis. A good example of this is a sub-woofer vs. a tweeter. Bass is low frequency sound and you can hear it for a long ways, it shakes your car. But no one ever complains about a neighboring cars mids or tweeters because higher frequencies do not travel as well or shake other objects. This is the same principal for that annoying engine harmonic.
The balance shaft is an out of balance rod that can create a harmonic to counter the feel of the inherent engine shake. The balance shaft is statically balanced so it will roll smooth but it is dynamically out of balance with weight on one end and an opposing weight 180 degrees off on the other. This is done on purpose to cancel out the vibration inherent to a 90 degree V6 cylinder engine. Mainly, its work at idle and at low engine speeds where vibrations are felt the most. It does not keep your engine in balance; in fact it is purposely out of dynamic balance which is bad for performance. The trade-off is worth it for the average consumer. The real problem comes when you want to use the engine at high engine speeds. Remember the math above about forces as they are related to rpm? It just so happens that the radius of a factory balance shaft is just over an inch but the out of balance (counter weight) is a lot more than an ounce! This causes terrible internal engine shake and HP being used to create this vibration. For high rpm engine operation, it is recommended to eliminate or disable the factory balance shaft.