Question: Use the assumed modes method with trial functions [ w_{1}(x)=x(x-L) quad w_{2}(x)=x(x-L)^{2} quad w_{3}(x)=x(x-L)^{3} ] to approximate the two lowest natural frequencies and mode shapes

Use the assumed modes method with trial functions

\[ w_{1}(x)=x(x-L) \quad w_{2}(x)=x(x-L)^{2} \quad w_{3}(x)=x(x-L)^{3} \]

to approximate the two lowest natural frequencies and mode shapes for a simply supported beam.

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