I bought a '75 Triumph Trident 750 triple once, and after I "woke it up" (carb cleaning, new battery, plugs, oil change, etc), I took it out Hwy 59 leaving Laredo, to a couple of nice long stretches to open it up and see how it felt.
Everything was going great 'till about 70 when it started to weave; it's straight 2-line with wide shoulders, so I wasn't really too concerned. I figured I'd wick it up and see if it got better - it didn't.
At about 80, the weave became a high-speed wobble, and the rear tire was leaving long black opposing scallops on the roadway! I still had my wits about me, so I un-clenched my hands to "give it it's head" - that didn't work either. I JUST started to apply a bit of rear brake and immediately realized that was NOT a good solution, as the weaving became more furious.
Next I started easing off the throttle, at which point I got into a WILD tank-slapper! I was already down though the low 70s as I started easing over toward the shoulder in case I had to bail, I figured it would be a softer landing in the tall buffel grass. The road started up a fair incline around this time, so without ever touching the brakes, I was able to scrub off a good amount of speed.
I was still almost knocking dents in the tank with my knees, but miraculously nothing bad happened as the bike seemed to settle down about 65, then smoothed out again at 60. Thankfully, no traffic in either direction the entire time, and the big curve in the road was just ahead. I pulled over, took a couple of deep breaths, thanked God I was OK, then flipped it around and rode home.
As soon as I got home, I jacked the bike up and started looking at the wheels - nothing obvious. Then I reached for a screwdriver and started tapping spokes - ALL THE REAR SPOKES WERE LOOSE! It turned out the previous owner had the wheels re-laced with stainless spokes by a local guy who neglected to tighten them up properly!
Yeef.