The theory says that stiffness acts in the same way as an out of balance wheel, the centre of the wheel mass describes a circle around the centre of rotation.
The vibration of an out of balance wheel is caused by that wheel circle being deflected by the impact with the road surface.
So set up your test rig with a variable rigid weight and measure the deflection between hard and soft axles at varying speeds.
Some one else can do the math but I know that 40 grams static wont measurably defelct an axle, but 40 grams out of balance at 2000 axle RPM can certainly deflect the axle (remember, the vibration is that difference between centre of wheel rotation and centre of axle rotation hitting the road).
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