It's AumSum Time.
Why do Airplane Wings Wobble?
Simple.
Because I keep on shaking them.
Oh AumSum.
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When an aircraft is flying at a constant speed and at a constant altitude then the same amount of force will be pushing it up as well as down.
i.e. the net force will be zero.
Now if the plane enters an area of higher air density say a large cloud then this would lead to an increase in the force pushing it up.
i.e. lift force will increase.
As a result the plane is pushed upwards and its wings temporarily bend up in the process.
Now if the plane enters an area of lower density.
i.e. it comes out of the cloud then the lift force is reduced, as a result the plane comes down, its wings bend back down.
This sudden change in lift force is what causes the plane wings to wobble.