Railways Technical Ability Vibration Analysis Question Bank Vibration Analysis

  • question_answer A machine of 100 kg mass has a 20 kg rotor with 0.5 mm eccentricity. The mounting springs have stiffness 85 kN/m and damping is negligible. If the operating speed is \[20\pi \] rad/and the unit is constrained to move vertically, the dynamic amplitude of the machine will be:

    A) \[0.170\times {{10}^{-\,4}}m\] 

    B) \[1.000\times {{10}^{-\,4}}m\]

    C) \[1.274\times {{10}^{-\,4}}m\] 

    D) \[2.540\times {{10}^{-\,4}}m\]

    Correct Answer: C

    Solution :

    \[{{\omega }_{n}}=\sqrt{\frac{k}{m}=\sqrt{\frac{85\times {{10}^{3}}}{100}}}=29.15\,\,\text{rad/s}\] \[\omega =20\pi \,\,\text{rad/s}\] \[\beta =\frac{\omega }{{{\omega }_{n}}}=\frac{20\,\pi }{29.15}=2.155\] \[\mu =\frac{20}{100}=0.2\] \[X=\frac{\mu e{{\beta }^{2}}}{{{\beta }^{2}}-1}=\frac{0.2\times 0.5\times {{(2.155)}^{2}}\times {{10}^{-\,3}}}{{{(2.155)}^{2}}-1}\] \[=1.274\times {{10}^{-\,4}}m\]

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