All gas engines have some vibration simply by the up/down movement, severe vibration is caused from an imbalance, in the cheapo 2-stroke engines it is usually the crank shaft but it could easily be the piston or rod or even the bearings if it uses them, the really cheap kits use bushings!
It could also be caused by misfiring or poor fuel mix.
Vibration grows force exponentially.
This is easy to see in an upright washing machine with an unbalanced wet load on spin cycle.
It grows until the washer starts walking around to dissipate the force.
With a washing machine you just balance the load, or bolt it to the floor and force the machines bearings to dissipate it that way.
For an engine all you can do is balance it, or dissipate it through the bike frame.
In short, make the engine one with the bike frame.
Hose clamps work well when they are around something round and straight.
They don't care for bends and angles and tend to slip and loosen so keep an eye on them.
A fine safety feature though!
Give your engine mount the 'shove test'.
Grab your top bar over the engine with 1 hand, and grab your engine head with other hand and
then try to shove your engine back and forth AS HARD AS YOU CAN.
If it moves in the frame AT ALL that is a fail.
Even a little vibration will grow if not 'bolted to the floor', in this case the frame.
That will keep the vibration from growing and breaking things.
That means the vibration is in the bike itself now and why you have to really secure everything so it doesn't feed the vibration.
You dissipate some of vibration through the handlebar grips.
That is where I dissipate vibration before my hands, at the grips.
The very first thing I hated about my very first build was the kits hard plastic grips, so that was the very first thing I had to change.
The most annoying thing between the bike and I was the grips.
I use pretty much generic BMX grips, which are simply black pipe insulation but a bit denser and the packs have end caps and rounded edges, and they
stretch.
The plastic throttle barrel is bigger outside than a regular grip is inside.
I just use a utility knife to cut down the length of the throttle barrel grip and peel it off of the plastic throttle barrel, and throw both grips in a box.
A little soapy water and you can massage a foam grip over the throttle barrel.
The left side of course fits easy and pretty darn good at dampening out vibration before it hits your hands.
So good, by my hands assessment, I haven't used hard plastic kit grips on my builds dating back to this one in 2010.
~$12 for enough to replace the foam a couple of times as they don't hold up to weather well.
Just a tip, another is pull that skinny spring off you clutch cable between the arm and cable stop.
It's sole purpose in life is to make your clutch lever harder to pull ;-}
