Restoring Force in Speed Wobble's on bicycles [URGENT]

Jan 2020
I've been looking into speed wobbles. A speed wobble is when at high speeds if a bike's wheel is suddenly deflected to the left for example, bike will twist it back to the right to straighten it (because of something called trail). But the wheel has weight and momentum, so it can overshoot and go past the center line. So now it’s turned to the right. Again the bike tries to turn the wheel back again, and it overshoots again and it keeps going back forth like that until the bike loses control). I'm trying to find an equation to fit this description but I can't seem to find any. I know that there is a similarity between this and a simple pendulum but a simple pendulum operates vertically while this operates horizontally and no gravitational force is acting on it. Any help is appreciated.
Apr 2015
Somerset, England
The wheel has mass, linear momentum and (significant) angular momentum.

It is the combination of linear and angular momenta that create the gyroscopic force which cuases the resotring correction.
(the initial deviation is caused by unven ground, a stone etc)

Consider a rotating body moving along a line AB with uniform angular velocity omega and unform linear velocity V

This creates a gryroscopic acceleration alpha as shown

\(\displaystyle \alpha = 2V\Omega \)


Full analysis of this is beyond high school mechanics.
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