Resonant frequency is the frequency at which an object "rings"
if it is moved. When you hit a tube with a hammer, and listen at
the end of the tube, you are hearing the audible portion of its
resonant frequency spectrum. The "fundamental" is the lowest note.
In handlebars, this is the frequency made by the bars "flapping."
By flapping I mean that the bar clamps stay put, while the tips
move most. This fundamental frequency is typically the strongest
frequency, thus the first one to attack. Weights on the tips of the
bars reduce vibration by moving the resonant frequency lower, away
from the frequencies generated by the engine. This happens for the
same reason that a heavier guitar string sounds lower, under the
same tension, than a lighter one. Because the effectiveness of a
weight in reducing vibration this way reduces to zero as the weight
approaches the bar clamp, I was careful to keep as much weight
outboard of the bar ends as possible. All the weight is
concentrated where it is most effective- right near the bar-ends.
All the weight is within 2.5" of the bar ends. There's no dead
weight as with solutions that go all the way through the bars. By
moving the resonance lower, it typically moves further from the
frequency of the engine, which reduces the build-up of vibration in
the bars dramatically. The other way to look at it is in terms of
inertia. By solidly mounting the weights to the ends of the bars,
the bar-ends gain a great deal of inertia, which means that they
are much more reluctant to change speed. Since the flapping motion
involves the bar ends accelerating this way and that in rapid
succession, any weight on the ends reduces this motion. When you
are trying to contain vibration by changing the resonant frequency,
solid-mounting is the way to go. Any flexibility to the mounting
muddies the effect of the extra weight, hurting the cause.