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(D) For two identical springs of constant $k$ connected in series,the equivalent spring constant is $k_s = \frac{k \cdot k}{k + k} = \frac{k}{2}$.The

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$1:2$

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(D) For two identical springs of constant $k$ connected in series,the equivalent spring constant is $k_s = \frac{k \cdot k}{k + k} = \frac{k}{2}$.The frequency of oscillation in series is $f_s = \frac{1}{2\pi} \sqrt{\frac{k_s}{m}} = \frac{1}{2\pi} \sqrt{\frac{k}{2m}}$.For two identical springs of constant $k$ connected in parallel,the equivalent spring constant is $k_p = k + k = 2k$.The frequency of oscillation in parallel is $f_p = \frac{1}{2\pi} \sqrt{\frac{k_p}{m}} = \frac{1}{2\pi} \sqrt{\frac{2k}{m}}$.The ratio of their frequencies is $\frac{f_s}{f_p} = \frac{\frac{1}{2\pi} \sqrt{\frac{k}{2m}}}{\frac{1}{2\pi} \sqrt{\frac{2k}{m}}} = \sqrt{\frac{k}{2m} \cdot \frac{m}{2k}} = \sqrt{\frac{1}{4}} = \frac{1}{2}$.Thus,the ratio is $1:2$.

Two identical springs of constant $k$ are connected in series and then in parallel. $A$ mass $m$ is suspended from them,the ratio of their frequencies of vertical oscillations will be

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