Railways Technical Ability Vibration Analysis Question Bank Vibration Analysis

  • question_answer A shaft carries a weight W at the centre. The CG of the weight is displaced by an amount e from the axis of the rotation. If 'y is the additional displacement of the CG from the axis of rotation due to the centrifugal force, then the ratio of y to e (where \[{{\omega }_{c}}\] is the critical speed of shaft and \[\omega \] is the angular speed of shaft) is given by:

    A) \[\frac{1}{{{\left[ \frac{{{\omega }_{c}}}{\omega } \right]}^{2}}+1}\]              

    B) \[\frac{1}{{{\left[ \frac{{{\omega }_{c}}}{\omega } \right]}^{2}}-1}\]

    C) \[{{\left[ \frac{{{\omega }_{c}}}{\omega } \right]}^{2}}+1\]                 

    D) \[\frac{\omega }{{{\left[ \frac{{{\omega }_{c}}}{\omega } \right]}^{2}}-1}\]

    Correct Answer: B

    Solution :

    \[\frac{y}{e}=\frac{{{\beta }^{2}}}{1-{{\beta }^{2}}}=\frac{1}{{{\left( \frac{{{\omega }_{c}}}{\omega } \right)}^{2}}-1}\]

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