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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