Free-free bar
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A free-free bar is an idealized bar that is completely free to vibrate at both ends without external constraints.[1] A marimba or xylophone bar can be modeled by this. Free-free bars are highly inharmonic, and their vibration is governed by a complex differential equation which can be solved to determine the spectrum of a free bar.[2] The n-th overtone of a free bar can be approximately represented by the formula below.[3]
\begin{displaymjx}f_n = 0.441 \left( n + \frac{1}{2} \right) ^2 f_1\end{displaymjx}
where f1 is the fundamental frequency.
See also
References
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