Bearman, et al. (1987) in his paper: EXPERIMENTS ON FLOW-INDUCED VIBRATION OF A SQUARE-SECTION CYLINDER, outlines his method of calculating Effective Mass as follows:

"The effective mass of the moving system (Mass oscillating on springs) was deduced by observing the natural frequency of the model with an additional mass m added to it. Plotting m against 1/Wn^2, where Wn, is the corresponding circular natural frequency of vibration, the effective mass of the model above can be found by dividing the average slope of the curve (which is equal to the stiffness of the system) by its intercept at m = 0 (which is equal to the inverse of the square of the natural frequency of the model alone).."

From the above:

effective mass = Slope / x-intercept at m = 0

= (m/(1/Wn^2)) / (1/Wn^2)

= (m x Wn^2) / (1/Wn^2)

= m x Wn^2 x Wn^2

which looks weird to me because Wn^2 should cancel out to get the effective mass.

Am I overlooking something here? Any leads on the matter are appreciated. Thanks.