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Power stroke from release to launch.

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One aspect of the power stroke that I know I don't understand but would like to, is the part where the string goes tight or straight; somewhere around brace height I suspect.
Quite often the limbs seem to wobble at the end; sometimes that is quite violent and noisy and we try to correct it with brace height changes etc.
If I could show a really slomo version of this, I think we would see one limb carrying on a bit further than the other, and then rebounding, letting that other limb go forwards, and both end up see sawing for a while.
I have read that the limb that carries on further still has more stored energy in it than the other. I can understand that up to a point. With more energy still in it, that limb will over power the other when the string goes tight. The energetic limb will carry on and work on the weaker limb; pulling that limb back slightly. We can mimic this with the bow braced, by pulling one limb tip back and seeing the other limb move the other way.
The bit I don't understand is why the more energetic limb has more energy still it and how that energy gets there. Put another way, when the limbs move forwards on the power stroke, they will both start losing energy(?? )and gaining speed. Or are they gaining energy by moving faster??
At full draw there is a point where the forces are in equilibrium and things settle to a sort of "at rest" state; bow balancing archer's draw force. Are the two limbs storing equal amounts of energy at that stage?
I understand that on release, things change and the arrow has to be moved, and that takes energy.
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