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I'm looking at getting an 81 sportster and when I went for a test ride I could push on the handle bars and if felt like I was pushing the entire front assy forward like the goose neck area was out of wack. Is there a simple tightening I can to do tighten it up so it's not so soft and stiffen it up to make it feel better?
There are rubber bushings, part number 56158-73, between the risers and the frame. These become worn and the handle bar has a lot of flex. You can replace them. Replacements are readily available from an indie motorcycle shop, J&P Cycle, etc. They come in different materials so you can get solid or simply firm ones. You will need to do some research to determine what to get. Someone else here may know more.
What IronMick said plus check for a cracked riser. I had a riser crack on the bottom and it had some wobble to it. The OEM risers were die cast aluminum so over tightening could bust them.
I should have my bushing replacement kit in today from my local bike shop, I'll double check the riser but I think it will be the bushings well at least I pray it is.