Estimate the fundamental frequency for the longitudinal vibration of a uniform bar fixed at (x=0) and free
Question:
Estimate the fundamental frequency for the longitudinal vibration of a uniform bar fixed at \(x=0\) and free at \(x=l\) by assuming the mode shapes as
(a) \(U(x)=c_{1}(x / l)\) and
(b) \(U(x)=c_{1}(x / l)+c_{2}(x / l)^{2}\).
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