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The dreaded steering wobble, or shake. It has a lot to do with the geometry of the front end of the motorcycle. Lots of bikes experience it. Some old models even went as far as to incorporate a steering dampener shock. I've seen them on some older small bikes. Goldwings seem to be prone to it under certain conditions. Probably because it's a heavy bike, so it puts more weight on the steering head.
Most people that experience it, complain of it while decelerating between 35 mph and 25 mph. Especially if they take both hands off the handlebars at the same time. Almost always, if at least one hand is on the handle bars, it dampens the steering enought that you won't get a wobble. But on one occasion I experienced a force strong enough that required both hands to stop it. (I was run off the road and I jumped a curb going back on the road.)
There are lots of opinions as to what causes it, but it has to do with the self righting forces of the motorcycle (hence the geometry). When something pushes the wheel off center, the bike wants to re-center itself and the wheel goes back to center, but it over corrects and then it's pointing to the other side. So it re-centers itself but over corrects again. It sets up an oscillation and the wheel goes back and forth. Depending on the conditions, the oscillation can grow worse with each swing of the wheel, that is unless another force is there to dampen it. Without something to dampen it, you get the tank slapper. If nothing else is there to stop it, your hands are your last defense. So when you take both hands off the handle bars, all it takes is a small bump and away it goes.
The first time it happened to me, it scared the daylights out of me. I wasn't ready for it and I thought the bike had a major mechanical problem. I talked to an experienced friend at the Honda shop. I was embarrased to admit that I was riding no handed. She laughed and told me to keep my hands on the handle bars. Then she explained that actually it's a common thing and many many people had told the same story before me.
Several things are known to affect it.
First check your tires. Tires that are abnormally worn, or out of balance are more likely to set up the wobble conditions. It doesn't happen as often with new tires. But you shouldn't have to replace your tires early just to stop the wobble. The tires don't cause the problem, they just set up that bump that is needed to start the shake.
Because of my own experience, I am a big believer in the importance of the adjustment of the steering head bearings. It's probably the best thing you can do for the situation. I'm not saying loose steering head bearings cause the problem, and I'm not saying tight steering head bearings solve the problem. But I am saying that it makes a big difference. If they are too loose, it's just that much easier for the wheel to swing back and forth. If the steering head bearings are well adjusted, they will offer some dampening to the steering, and help overcome the bikes tendency toward the steering wobble.
My personal experience with my 1200 was that it wobbled rather easily. I just learned to live with it. I didn't know much about it at the time. After a couple years, when the bearings wore out, I knew they needed to be replaced because I could feel a "notch" in the steering, so I replaced them. I did it myself, and I muddled my way through the job. I didn't know how to properly torque them so I did it by trial and error. It took three tries. The first time they were too tight, and the bike tended to wander as the steering was too slow to return to center. So I loosened them up and then it wanted to wobble really easily. So I tightened them a little bit and I think I got them pretty well right. The bike felt really good, and I didn't experience a steering wobble again for about 2 years. That notch I felt means the bearings are shot. They will be loose long before they are worn out. Maybe by a few years. So if your front end is loose, that doesn't mean you need to replace your bearings. It could just be time to tighten them up a little bit.
If you want to test it, get out on a side road where there isn't any traffic at all. Go about 25-30 mph. Take both hands off the handle bars and then lightly slap one of the hand grips. If it starts to wobble and the wobble grows quickly, it's time to make some adjustments. If it's really loose, it will wobble really bad, really quickly so be ready to grab the bars. Intentionally inducing a shake isn't exactly one of the safer road test items you can do, so be careful.
Somebody posted an article here once, a really good write up about how to tighten them correctly to ensure the bearings reseat properly. I saved the link for just such an occasion:
http://www.motorcycleproject.com/motorcycle/text/shucking.html