Railways Technical Ability Vibration Analysis Question Bank Vibration Analysis

  • question_answer The natural frequency of transverse vibration of a massless beam of length L having a mass m attached at its midspan is given by:       (El is the flexural rigidity of the beam)

    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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