Two identical springs of spring constant k each are connected in series and parallel as shown in figure. A mass M is suspended from them. The ratio of their frequencies of vertical oscillation will be

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2 : 1

4: 1

1: 4

1: 2

answer is A.

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Detailed Solution

$k_{s} = \frac{k \times k}{k + k} = \frac{k}{2}$

$k_{p} = k + k = 2 k$

$∴ \frac{n_{s}}{n_{p}} = \frac{\frac{1}{2 π} \sqrt{\frac{k_{s}}{M}}}{\frac{1}{2 π} \sqrt{\frac{k_{p}}{M}}} = \sqrt{\frac{k_{s}}{k_{p}}} = \sqrt{\frac{k / 2}{2 k}} = \frac{1}{2}$

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