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In the figure shown, rod AB is light and rigid while rod CD is also rigid and hinged at its midpoint O. Rod can rotate without friction about O. The time period of small oscillation of rod CD is $T = 2 π \sqrt{\frac{m}{n k}}$ where m is mass of rod CD and k is spring constant of each spring. The value of n is

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answer is 5.

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Detailed Solution

$\frac{m l^{2}}{12} α = - {\frac{2 k θ}{12} + \frac{k θ}{4}} l^{2} \Rightarrow α = - (\frac{5 k}{m}) θ$

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