A thin bar of length (l) and mass (m) is clamped at one end and free at
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A thin bar of length \(l\) and mass \(m\) is clamped at one end and free at the other. What mass \(M\) must be attached to the free end in order to decrease the fundamental frequency of longitudinal vibration by \(50 \%\) from its fixed-free value?
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