As shown in the figures, a uniform rod OO ′ of length l is hinged at the point O and held…

As shown in the figures, a uniform rod OO′ of length l is hinged at the point O and held in place vertically between two walls using two massless springs of same spring constant. The springs are connected at the midpoint and at the top-end (O′) of the rod, as shown in Fig. 1 and the rod is made to oscillate by a small angular displacement. The frequency of oscillation of the rod is f₁. On the other hand, if both the springs are connected at the midpoint of the rod, as shown in Fig. 2 and the rod is made to oscillate by a small angular displacement, then the frequency of oscillation is f₂. Ignoring gravity and assuming motion only in the plane of the diagram, the value of \(\frac{f_{1}}{f_{2}}\)is
\[\begin{array}{l} \text { Fig. } 1\\ \text { Fig. } 2 \end{array}\]