Calculating the Natural Circular Frequency, Period, and Frequency of a Simply Supported Beam with a Concentrated Load at Any Point Along its Length

February 23, 2017 Abdul Siraj, P.E.

In this post, I will discuss the fifth 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 simply supported beam with a concentrated load at any point along its length.


The problem statement states,


A cantilevered beam having a concentrated weight at the given location 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′
a = 15′
b = 5′



Abdul Siraj, P.E.