Calculating the Natural Circular Frequency, Period, and Frequency of a Cantilevered Beam with a Concentrated Load at the End

February 23, 2017 Abdul Siraj, P.E.

In this post, I will discuss the second example in our structural dynamics course covering undamped free vibration. The goal of this structural dynamics example is to calculateĀ the natural circular frequency, period, and frequency of a cantilevered beam with a concentrated load at the end.


The problem statement states,


A cantilevered beam having a concentrated weight at its end is shown below.

Assume: Mass of beam negligible in comparison to mass of concentrated weight and neglect effects of damping.

Determine equation of motion, natural circular frequency, period, and natural frequency


Let W = 10 kips,
I = 200 in^4,
E = 29,000 ksi,
L = 20′



Abdul Siraj, P.E.