Compute the fundamental natural frequency of the transverse vibration of a uniform beam of rectanqular cross section, with one end of the beam is free and one end is fixed. the cross section has a base of 100 mm and height of 300 mm, length of the beam is 5.9 m, e=20.5x10^10 n/m2 and density of 7830 kg/m3. write your answer in rad/sec with 2 decimal points.

The natural angular frequency of the rod is 53.56 rad/sec

Explanation:

Since the beam is free at one end and fixed at the other hence the beam is a cantilevered beam as shown in the attached figure

We know that when a unit force is placed at the end of a cantilever the displacement of the free end is given by

Hence we can write

Comparing with the standard spring equation we find the cantilever analogous to spring with

Now the angular frequency of a spring is given by

where

'm' is the mass of the load

Thus applying values we get