A) \[{{\left( \frac{m{{l}^{3}}}{48EI} \right)}^{\frac{1}{2}}}\text{rad/s}\]
B) \[{{\left( \frac{48m{{l}^{3}}}{EI} \right)}^{\frac{1}{2}}}\text{rad/s}\]
C) \[{{\left( \frac{48EI}{m{{L}^{3}}} \right)}^{\frac{1}{2}}}\text{rad/s}\]
D) \[{{\left( \frac{3EI}{m{{L}^{3}}} \right)}^{\frac{1}{2}}}\text{rad/s}\]
Correct Answer: C
Solution :
\[k=k=\frac{48EI}{{{l}^{3}}}\] \[{{\omega }_{n}}=\sqrt{\frac{k}{m}}=\sqrt{\frac{48EI}{m{{l}^{3}}}}\]
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