Rayleigh's Method for Determining Fundamental:

Natural Frequency

In this, first the actual loads are corrected by adding up weight of half of the free segments of the shaft to them. In order to describe this further a shaft system illustrated in Figure 14 might be supposed.

To correct W₁, add up half of the load if segment AB and half of the segment BC. Likewise to accurate weight W₂ half of the load of segment BC & half of the segment CD may be adding up to W₂. It is complete to take weight of the shaft/beam into account. Once this is done an Equation can be utilized.

This equation shall determine value of w_n after putting weight 'W₁' and deflection 'y_i' under it. The deflections also may be resolute using corrected loads.