Analysis vs Staad Uniform loaded cantilever beam

Hello

As part of my project I had been going through some examples as shown on the verification manual of Staad Pro v8i and version 2007. However, I been having issues with some of the examples as some do not show the full detail of calculation description.

The one example been having problem with from Staad 2007 VM is on DYNA-Beam 4 where you must calculate the first 3 natural frequencies of the cantilever thats split up into 20 members. Using the reference mentioned I assume the equation that is being used is the following:

\omega_i = 2 * \sqrt{\frac{AEN^2}{ML}} * sin(\frac{(2i - 1) * \pi}{4 N})

Assuming
N = 20
L = 80 in
w = 1.124 lb/in
A = 4 in^2
I = 1.33333 in4
g = 386.4 in/sec2
E 30000ksi

M = (1.124/386.4) * 80

According to the example and the staad solution the 3 frequencies are as follows:

f1 = 10.237

f2 = 63.974

f3 = 178.67

Is it possible that you could clarify/correct my approach?