A uniform cantilevered beam is given in the figure below, with the flexural rigidity $EI,$ the length $L$

and the mass per length $/bar(m).$ A lumped mass $\frac{?}{b}=ar(m)L$ is placed at the free end of the beam. Three

shape functions are given as: $($a$)(x)=\frac{x}{L}(\frac{x}{L}-1)$;

$($b$)(x)=1-cos\frac{x}{2L}$;

$($c$)(x)=\frac{3x^2}{2L^2}-\frac{x^3}{2L^3}$

Question: By Rayleigh's method estimate the natural vibration frequency of the cantilevered

beam with the best shape function.

$L,EI\frac{,}{b}ar(m)$

Mass $=w$