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Found this: https://electronics.stackexchange.com/questions/253607/why-weights-on-cables-between-utility-poles
Probably some combination of electromagnetic effects in that specific section. Happens to oscillate just right. Though these weights can be used for wind issues, I'm seeing a lot of references to dampening other kinds of vibrations. Might help you find a better answer.
Hmm. It's odd that this isn't ALWAYS vibrating, but it IS only between these two poles that I've noticed the vibration. But why not between other sets of poles? And since the cable vibrating the most isn't a power cable (I believe it's fiber, but it could be copper - but it's definitely telecom, since it's not insulated on the top crossbar, as the other power cables are), it can't really be much power going through it. I'm kind of hoping someone else has seen similar behavior somewhere else. You can see the anti-wind-twist devices (don't know what else to call them) bolted to the other telecom cable (sort of diamond-shaped) and they will cause the cable to stabilize when the wind is really blowing, but you can see the wind isn't blowing at all, and the cable continues to vibrate quite noticeably. I really do hope someone else has seen something like it elsewhere...
In regards to it only being between those two poles, I'd wager it simply comes down to tension. The other cables are tensioned correctly and this section is either too loose or intentionally loose as some sort of expansion/contraction relief.