states that the buoyant force is equal and opposite to the force of gravity acting on the bob. As long as this is the case, the bob will not become any more or less submerged than it already is. We can also write this equation as

which is to say that as long as the ratio between the two forces is exactly 1, the bob will remain in the same position relative to the water. Notice in the above equation that g can be canceled out of the numerator and the denominator, which means that the ratio of the two forces is independent of the value of g. This is a bit startling: it means that the submerged volume would stay exactly the same no matter what the local gravitational acceleration is (so long as there is some non-zero gravity).

When the system begins to exhibit simple harmonic motion, it moves up and down rhythmically, and when the spring is pulling the bowl up it must exert a force equal to the weight of the system in addition to the force which accelerates the bowl upward. This additional force has the effect on the system of an increased value for g. When the spring is allowing the the bowl to drop, it is applying a force on the system which is less than the weight of the system, and this reduced force has the effect on the system of a decreased value for g. If the oscillations aren't too wild, then this artificial value for g will always be positive (otherwise the water will splash out of the bowl and the fish may become ill). This means that the buoyant force acting on the bob will always exactly balance the downward "gravitational" force acting on the bob in the frame of reference of the bowl. The forces acting on the bob are not balanced in an inertial laboratory reference frame (clearly, the bob is accelerating), but they are balanced in the frame of reference of the bowl, and so the bob does not accelerate with respect to the bowl or the water contained therein. The bob's level of submergence never changes.

What of the fish? The arguments given above are valid for the fish also, insofar as to say that the fish will not change its position in the water as a result of the oscillations of the system, but that is not to say that the fish will not feel anything. The fish is accelerating, and this requires that a force be applied to it. Even though in the frame of reference of the bowl the forces acting on the fish are balanced, the buoyant force and the "gravitational" force are changing, and the fish will feel these changes. Consider this: intuitively, it may appear that if the bob does not change its level in the water then the fish must not feel the effects of changing g, but if this were really the case then we could simply submerge astronauts in tubs of water before firing the rockets which propel them into orbit and the astronauts would not feel the discomfort of the acceleration. Sadly, we cannot shield people in this way from the effects of acceleration. If we could, then it would be more feasible to accelerate space travelers to near the speed of light.