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(C) The frequency of vertical oscillations for a spring-mass system is given by $n = \frac{1}{2\pi}\sqrt{\frac{k_{eq}}{m}}$.For springs in series,the

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$1:2$

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(C) The frequency of vertical oscillations for a spring-mass system is given by $n = \frac{1}{2\pi}\sqrt{\frac{k_{eq}}{m}}$.For springs in series,the equivalent spring constant is $k_S = \frac{K \cdot K}{K + K} = \frac{K}{2}$.The frequency in series is $n_S = \frac{1}{2\pi}\sqrt{\frac{K/2}{m}}$.For springs in parallel,the equivalent spring constant is $k_P = K + K = 2K$.The frequency in parallel is $n_P = \frac{1}{2\pi}\sqrt{\frac{2K}{m}}$.The ratio of their frequencies is $\frac{n_S}{n_P} = \sqrt{\frac{k_S}{k_P}} = \sqrt{\frac{K/2}{2K}} = \sqrt{\frac{1}{4}} = \frac{1}{2}$.

Two identical springs of constant $K$ are connected in series and parallel as shown in the figure. $A$ mass $m$ is suspended from them. The ratio of their frequencies of vertical oscillations will be

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