Merlin,then W1 =1/2 F*x1 and W2=1/2 F*x2.
It is probably a typo of some sort but I get x1=F/k1 and x2=F/k2. Thus W1=1/2*k1*(F/k1).^2 and W2=1/2*k2*(F/k2).^2. Consequently W1=\(1/2*F^2/k1\) and W2=\(1/2*F^2/k2\) .
Result remains the same, i.e. W2>W1.
Agreed. I suspect the faster unloading of the higher frequency rod is the primary reason it produces more tip speed.However a key parameter is the “loaded” speed of the rod and that involves rod action somewhere. Faster rods are more on the tip action side and can remain faster under load by comparison to softer / butt action rods. This influences tip speed.
Gordy