A concentrated mass m is attached at the centre of a rod of length 2L as shown in the figure. The rod is kept in a horizontal equilibrium position by a spring of stiffness k. For very small amplitude of vibration, neglecting the weights of the rod and spring, the undamped natural frequency of the system is:

• A. \(\sqrt {\frac{k}{m}}\)
• B. \(\sqrt {\frac{{2k}}{m}}\)
• C. \(\sqrt {\frac{k}{{2m}}} \)
• D. \(\sqrt {\frac{{4k}}{m}}\)