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$F=m*a$ accounting for pressure wave propagation

$m$ is the mass of your “system” and $v$ is the velocity of the center of mass of the system. The system could be the whole rod or some subset of the rod. The easiest is the whole rod. If it is a ...
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Confusion in Derivation of Excess Pressure in a Cylindrical Drop

Simple Answer: Assume that $l>>R$. You will get the answer in single step. Complicated Reality: Liquid would not form cylendrical shape on its own. The ends are not going to be flat plates that ...
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Confusion in Derivation of Excess Pressure in a Cylindrical Drop

That's a good start, however there are some subtleties behind treating surface tension as a force. Indeed, there are some classic problematic cases that are often overlooked at first. The best way to ...
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Inconsistent units in modal analysis of vibrating beam

I get the following eigenvectors: $$\mathbf v_1= \left[ \begin {array}{c} 1\\ {l}^{-1}-1/3\,{\frac { 1}{l\eta}}-1/3\,{\frac {\sqrt {9\,{\eta}^{2}+3\,\eta+1}}{l\eta}} \end {array} \right] ; \\ \mathbf ...
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