Problem B$-3-12$

In the mechanical system shown in Figure $3-42,$ assume that the rod is massless, perfectly rigid, and pivoted at point $P.$ The displacement $x$ is measured from the equilibrium position. Assuming that $x$ is small, that the weight $mg$ at the end of the rod is $5$ N $,$ and that the spring constant $k$ is $400\frac{N}{m},$ find the natural frequency of the system.