## 5 Results and Discussion
\begin{table}
\begin{tabular}{l l l l} \hline \hline \multirow{2}{*}{\(B\), \(\gamma\) = 1.67} & \multirow{2}{*}{\begin{tabular}{l} **First Critical Speed** \\ **Amplitude Value** \\ \end{tabular} } & \begin{tabular}{l} **Second Critical** \\ **Speed** \\ **Amplitude Value** \\ \end{tabular} & \begin{tabular}{l} **Third Critical Speed** \\ **Amplitude Value** \\ \end{tabular} \\ \hline \(b_{m}=0\) & 0.118574461, \(\tau=0.16\) & 0.27197385, \(\tau=0.61\) & 2.395991343, \(\tau=2.61\) \\ \(b_{m}=0.5\) & 0.11856806, \(\tau=0.16\) & 0.271326026, \(\tau=0.61\) & 2.386092738, \(\tau=2.61\) \\ \(b_{m}=5\) & 0.118510785, \(\tau=0.16\) & 0.244571454, \(\tau=0.61\) & 1.657566825, \(\tau=2.61\) \\ \(b_{m}=25\) & 0.118263621, \(\tau=0.16\) & 0.108761599, \(\tau=0.61\) & 0.307975554, \(\tau=2.61\) \\ \(b_{m}=50\) & 0.117971542, \(\tau=0.16\) & 0.079987206, \(\tau=0.61\) & 0.141437807, \(\tau=2.61\) \\ \(b_{m}=100\) & 0.117443017, \(\tau=0.16\) & 0.058212949, \(\tau=0.6\) & 0.078056973, \(\tau=2.61\) \\ \(b_{m}=500\) & 0.115713077, \(\tau=0.16\) & – & – \\ \hline \multirow{2}{*}{\(D\), \(\gamma\) = 1.67} & \multirow{2}{*}{\begin{tabular}{l} **First Critical Speed** \\ **Amplitude Value** \\ \end{tabular} } & \
\begin{tabular}{l} **Second Critical** \\ **Speed** \\ **Amplitude Value** \\ \end{tabular} &
\begin{tabular}{l} **Third Critical Speed** \\ **Amplitude Value** \\ \end{tabular} \\ \hline \(b_{m}=0\) & 0.078416443, \(\tau=0.16\) & 0.319661082, \(\tau=0.61\) & 2.101480075, \(\tau=2.61\) \\ \(b_{m}=0.5\) & 0.078413261, \(\tau=0.16\) & 0.318899815, \(\tau=0.61\) & 2.092707266, \(\tau=2.61\) \\ \(b_{m}=5\) & 0.078385116, \(\tau=0.16\) & 0.286969287, \(\tau=0.61\) & 1.448573522, \(\tau=2.61\) \\ \(b_{m}=25\) & 0.078270549, \(\tau=0.16\) & 0.122332756, \(\tau=0.61\) & 0.248941102, \(\tau=2.61\) \\ \(b_{m}=50\) & 0.078151336, \(\tau=0.16\) & 0.064906783, \(\tau=0.61\) & 0.091711735, \(\tau=2.61\) \\ \(b_{m}=100\) & 0.077991713, \(\tau=0.16\) & 0.03343016, \(\tau=0.6\) & 0.034567932, \(\tau=2.61\) \\ \(b_{m}=500\) & 0.080131667, \(\tau=0.16\) & – & – \\ \(b_{m}=5000\) & 0.193818388, \(\tau=0.16\) & – & – \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Critical Speeds. \begin{table}
\begin{tabular}{l l l l} \hline \hline \multirow{2}{*}{\(B\), \(\gamma\) = 1.25} & \multirow{2}{*}{\begin{tabular}{l} **First Critical Speed** \\ **Amplitude Value** \\ \end{tabular} } & \
\begin{tabular}{l} **Second Critical** \\ **Speed** \\ **Amplitude Value** \\ \end{tabular} &
\begin{tabular}{l} **Third Critical Speed** \\ **Amplitude Value** \\ \end{tabular} \\ \hline \(b_{m}=0\) & 0.121638282, \(\tau=0.16\) & 0.122951082, \(\tau=0.59\) & 2.2814299046, \(\tau=3.02\) \\ \(b_{m}=0.5\) & 0.121632639, \(\tau=0.16\) & 0.122901957, \(\tau=0.59\) & 2.25145796, \(\tau=3.02\) \\ \(b_{m}=5\) & 0.1215826704, \(\tau=0.16\) & 0.121641647, \(\tau=0.59\) & 1.035804071, \(\tau=3.02\) \\ \(b_{m}=25\) & 0.121367604, \(\tau=0.16\) & 0.098499341, \(\tau=0.58\) & 0.166361948, \(\tau=3.02\) \\ \(b_{m}=50\) & 0.121120227, \(\tau=0.16\) & 0.078839058, \(\tau=0.58\) & 0.103151902, \(\tau=3.02\) \\ \(b_{m}=100\) & 0.120694759, \(\tau=0.16\) & 0.055532351, \(\tau=0.58\) & 0.06308127, \(\tau=3.02\) \\ \(b_{m}=500\) & 0.120406103, \(\tau=0.16\) & – & – \\ \(b_{m}=5000\) & 0.210144507, \(\tau=0.16\) & – & – \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Critical Speeds. to an increase in the amount of liquid in the cavity in this case is even more pronounced. For example, the second critical frequency in this case appears already at \(\tau=0.57\) and the third already at \(\tau=3.36\). This means that with an increase in filling, the second critical frequency shifts to the first critical frequency until it merges with it, whereas the third critical frequency shifts in the direction of increasing frequency to the right and is almost completely damped with an increase in the amount of fluid in the rotor cavity.