Question:

for the axially vibrating bar shown below:

$EA(x)=\frac{6}{5}EA[1-\frac{1}{2}(\frac{x}{l}{)}^2]$

$m(x)=\frac{6}{5}m[1-\frac{1}{2}(\frac{x}{l}{)}^2]$

Assume the boundary conditions are similar tb those of a uniform bar. Use the first mode shape of uniform bar as a trial function and estimate the fundamental frequency using the Ragleigh Quatient.