A concentrated mass $m$ is attached at the centre of the 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 every small amplitude of vibration, neglecting the weights of the rod and spring, the undamped natural frequency of the system is

1. $\sqrt{\dfrac{k}{m}} \\$
2. $\sqrt{\dfrac{2k}{m}} \\$
3. $\sqrt{\dfrac{k}{2m}} \\$
4. $\sqrt{\dfrac{4k}{m}}$