Two light identical springs of spring constant $k$ are attached horizontally at the two ends of a uniform horizontal rod $AB$ of length $l$ and mass $m$. The rod is pivoted at its center '$O$' and can rotate freely in horizontal plane. The other ends of the two springs are fixed to rigid supports as shown in figure. The rod is gently pushed through a small angle and released. The frequency of resulting oscillation is: (1) $\frac { 1 } { 2 \pi } \sqrt { \frac { 3 k } { m } }$ (2) $\frac { 1 } { 2 \pi } \sqrt { \frac { k } { m } }$ (3) $\frac { 1 } { 2 \pi } \sqrt { \frac { 6 \mathrm { k } } { m } }$ (4) $\frac { 1 } { 2 \pi } \sqrt { \frac { 2 k } { m } }$
Two light identical springs of spring constant $k$ are attached horizontally at the two ends of a uniform horizontal rod $AB$ of length $l$ and mass $m$. The rod is pivoted at its center '$O$' and can rotate freely in horizontal plane. The other ends of the two springs are fixed to rigid supports as shown in figure. The rod is gently pushed through a small angle and released. The frequency of resulting oscillation is:\\
(1) $\frac { 1 } { 2 \pi } \sqrt { \frac { 3 k } { m } }$\\
(2) $\frac { 1 } { 2 \pi } \sqrt { \frac { k } { m } }$\\
(3) $\frac { 1 } { 2 \pi } \sqrt { \frac { 6 \mathrm { k } } { m } }$\\
(4) $\frac { 1 } { 2 \pi } \sqrt { \frac { 2 k } { m } }$