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Figure shows a single degree of freedom system. The system consists of a massless rigid bar OP hinged at O and a mass $m$ at end P. The natural frequency of vibration of the system is

  1. $f_n=\displaystyle{\frac{1}{2\pi }\sqrt{\frac{k}{4m}}}$
  2. $f_n=\displaystyle{\frac{1}{2\pi }\sqrt{\frac{k}{2m}}}$
  3. $f_n=\displaystyle{\frac{1}{2\pi }\sqrt{\frac{k}{m}}}$
  4. $f_n=\displaystyle{\frac{1}{2\pi }\sqrt{\frac{2k}{m}}}$
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