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Display information for equation id:math.1255.191 on revision:1255

* Page found: Das d'Alembertsche Prinzip (eq math.1255.191)

Occurrences on the following pages:

Normalschwingungen Eq: math.1515.54

Hash: 8013a8ca8ab2186217fd94de27fb4ac6

TeX (original user input):

\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}

TeX (checked):

{\begin{aligned}&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{aligned}}

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MathML (4.914 KB / 575 B) :

\begin{aligned} 0 = \det (V_{l k} - ω^{2} T_{l k}) = m^{2} | \begin{matrix} \frac{g}{l} + \frac{k}{m} - ω^{2} & - \frac{k}{m} \\ \frac{- k}{m} & \frac{g}{l} + \frac{k}{m} - ω^{2} \end{matrix} | = 0 \\ 0 = ω^{4} - 2 (\frac{k}{m} + \frac{g}{l}) ω^{2} + \frac{g^{2}}{l^{2}} + 2 \frac{g k}{l m} = ω^{4} - 2 (\frac{k}{m} + \frac{g}{l}) ω^{2} + {(\frac{g}{l} + \frac{k}{m})}^{2} - {(\frac{k}{m})}^{2} \end{aligned}

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Identifiers

$V_{l k}$

$ω$

$T_{l k}$

$m$

$g$

$l$

$k$

$m$

$ω$

$k$

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$k$

$m$

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$ω$

$ω$

$k$

$m$

$g$

$l$

$ω$

$g$

$l$

$g$

$k$

$l$

$m$

$ω$

$k$

$m$

$g$

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$ω$

$g$

$l$

$k$

$m$

$k$

$m$

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