handlebar shakes

Doesn't happen on any of the bikes I keep. I had one or two where the handlebar would slip in the fork however much I tightened the top bolt, and I scrapped them.
Tap your spokes to see if any are loose. TIght ones go ping, loose ones go thud. You can use a crescent wrench to tighten them, I don't own a "spoke wrench". When the tire is off you can use a screwdriver on the end.
Axles can get loose, generally need a super thin 15 mm and or 17 mm wrench to tighten them. Inspect that no balls have dropped out if you find this. I made a super thin wrench by grinding a regular wrench thinner. Wear safety glasses using a grinder.
 
Check to see if the front wheel is true. Lift the front wheel off the ground and give it a spin. It is not normal for the handlebars to shake. Rear hub motor is not causing this.
 
I've never had handlebar shake occur on any of my rear hub ebikes. I do notice some slight vibration when riding on pavement with my knobby trail tires. This is normal though and can be minimized by lowering the tire pressure.
 
is this expected because of heavy rear hub motor

No, not normal at all, in any conditions.

I'm thinking if this is a new bike, you may not have the tire installed properly. As above, hold the front up and give the front tire a spin. Any tire issue will be obvious.

Just occrured to me you may be talking about a "vibration" in the handlebars (higher frequency shaking). Depending on the tread pattern of the tires, that might be normal if you have a knobby tread pattern, especially when running on pavement.
 
All the weight on mine is at the rear, i have experienced front wheel "float" especially when i lean back, no steering! as far as wobble goes that sounds like the the the front end is not tightened down enough?
I have aggressive tires but no shake even at high speeds, i have noticed it while walking the bike and a leaning it around a turn. mine are hybrid, on/off road so A could be right about the tires.
I had a cut sidewall and put a small piece of old tube in to seal it, it was like driving with a concrete wheel, everything was out of wack!
 
Something is amiss for sure, my step thru even at the occasional 28 mph does no shake at all. I would certainly find out before riding it though if something goes wrong that can cause loss of control it could be a disaster!
 
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