Hey come on.... ideally a bike's handle shouldn't oscillate to both sides on a decent road at any speeds, whether it is alloy/steel rim based.
I've personally experienced the oscillation OP has mentioned on my bike, and it has disappeared after I replaced the cone set.
There is some problem with his bike, please help him to sort it out.
Between, got the air filter changed today and carb tuned. Let me check the performance and mileage before fiddling with the carbon filled silencer...






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