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Display information for equation id:math.1515.54 on revision:1515

* Page found: Normalschwingungen (eq math.1515.54)

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\begin{align}
  & 0=\det ({{V}_{lk}}-{{\omega }^{2}}{{T}_{lk}})={{m}^{2}}\left| \begin{matrix}
   \frac{g}{l}+\frac{k}{m}-{{\omega }^{2}} & -\frac{k}{m}  \\
   \frac{-k}{m} & \frac{g}{l}+\frac{k}{m}-{{\omega }^{2}}  \\
\end{matrix} \right|=0 \\
 & 0={{\omega }^{4}}-2\left( \frac{k}{m}+\frac{g}{l} \right){{\omega }^{2}}+\frac{{{g}^{2}}}{{{l}^{2}}}+2\frac{gk}{lm}={{\omega }^{4}}-2\left( \frac{k}{m}+\frac{g}{l} \right){{\omega }^{2}}+{{\left( \frac{g}{l}+\frac{k}{m} \right)}^{2}}-{{\left( \frac{k}{m} \right)}^{2}} \\
\end{align}

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0 = det ⁡ ( V l ⁢ k - ω 2 ⁢ T l ⁢ k ) = m 2 ⁢ | g l + k m - ω 2 - k m - k m g l + k m - ω 2 | = 0 0 = ω 4 - 2 ⁢ ( k m + g l ) ⁢ ω 2 + g 2 l 2 + 2 ⁢ g ⁢ k l ⁢ m = ω 4 - 2 ⁢ ( k m + g l ) ⁢ ω 2 + ( g l + k m ) 2 - ( k m ) 2 missing-subexpression 0 subscript 𝑉 𝑙 𝑘 superscript 𝜔 2 subscript 𝑇 𝑙 𝑘 superscript 𝑚 2 𝑔 𝑙 𝑘 𝑚 superscript 𝜔 2 𝑘 𝑚 𝑘 𝑚 𝑔 𝑙 𝑘 𝑚 superscript 𝜔 2 0 missing-subexpression 0 superscript 𝜔 4 2 𝑘 𝑚 𝑔 𝑙 superscript 𝜔 2 superscript 𝑔 2 superscript 𝑙 2 2 𝑔 𝑘 𝑙 𝑚 superscript 𝜔 4 2 𝑘 𝑚 𝑔 𝑙 superscript 𝜔 2 superscript 𝑔 𝑙 𝑘 𝑚 2 superscript 𝑘 𝑚 2 {\displaystyle{\displaystyle\begin{aligned} &\displaystyle 0=\det({{V}_{lk}}-{% {\omega}^{2}}{{T}_{lk}})={{m}^{2}}\left|\begin{matrix}\frac{g}{l}+\frac{k}{m}-% {{\omega}^{2}}&-\frac{k}{m}\\ \frac{-k}{m}&\frac{g}{l}+\frac{k}{m}-{{\omega}^{2}}\\ \end{matrix}\right|=0\\ &\displaystyle 0={{\omega}^{4}}-2\left(\frac{k}{m}+\frac{g}{l}\right){{\omega}% ^{2}}+\frac{{{g}^{2}}}{{{l}^{2}}}+2\frac{gk}{lm}={{\omega}^{4}}-2\left(\frac{k% }{m}+\frac{g}{l}\right){{\omega}^{2}}+{{\left(\frac{g}{l}+\frac{k}{m}\right)}^% {2}}-{{\left(\frac{k}{m}\right)}^{2}}\\ \end{aligned}}}

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0=det⁡(Vlk−ω2Tlk)=m2|gl+km−ω2−km−kmgl+km−ω2|=00=ω4−2(km+gl)ω2+g2l2+2gklm=ω4−2(km+gl)ω2+(gl+km)2−(km)2

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