Question $05.$

L length horizontally setup $AB$ rigid rod was hinged at point $A$ so that it can freely move. A mass $m$ was attached at the end of the rigid road and two springs were attached vertically $\frac{L}{4}$ and $\frac{L}{2}$ from point $A$ so the rod maintains it horizontal position as shown in figure $03.$ Take spring stiffness as $k$ for both springs.

$($A$)$ Calculated the natural frequency of the systems if the mass of the rod was neglected.

$($B$)$ Calculated the natural frequency of the systems if the mass of the rod was $M.$