Talon Mcbride

2022-07-26

Get L by itself in the following equation
${f}_{n}=\frac{{m}^{2}\cdot \pi \cdot K\cdot v}{8\cdot {L}^{2}}$

Helena Howard

Expert

${f}_{n}=\frac{{m}^{2}\cdot \pi \cdot K\cdot v}{8\cdot {L}^{2}}$
Divide both sides by ${m}^{2}\cdot \pi \cdot k\cdot v\phantom{\rule{0ex}{0ex}}\frac{{f}_{n}}{{m}^{2}\cdot \pi \cdot k\cdot v}=\frac{1}{8\cdot {L}^{2}}\phantom{\rule{0ex}{0ex}}\frac{8{L}^{2}}{1}=\frac{{m}^{2}\cdot \pi \cdot k\cdot v}{{f}_{n}}\phantom{\rule{0ex}{0ex}}{L}^{2}=\frac{{m}^{2}\cdot \pi \cdot k\cdot v}{8{f}_{n}}$
take square root on both sides
$L=m\cdot \sqrt{\pi \cdot k\cdot \frac{v}{8{f}_{n}}}$

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