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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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