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)$\sqrt{\frac{4k}{m}}$ 