• # 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) $2.540\times {{10}^{-\,4}}m$

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