Fill in the Blank. For a shaft carrying masses (m_{1}, m_{2}, ldots), Rayleigh's method gives the natural
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Fill in the Blank.
For a shaft carrying masses \(m_{1}, m_{2}, \ldots\), Rayleigh's method gives the natural frequency as
\[\omega=\left\{\frac{g\left(m_{1} w_{1}+m_{2} w_{2}+\cdots\right)}{m_{1} w_{1}^{2}+m_{2} w_{2}^{2}+\cdots}\right\}^{1 / 2}\]
where \(w_{1}, w_{2}, \ldots\) denote the ___________ deflections of \(m_{1}, m_{2}, \ldots\), respectively.
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