Consider two identical

Consider two identical springs each of spring constant $\mathrm{k}$ and negligible mass compared to the mass $M$ as shown. Fig.1 shows one of them and Fig. 2 shows their series combination. The ratios of time period of oscillation of the two SHM is $\frac{T_{b}}{T_{a}}=\sqrt{x}$, where value of $x$ is

(Round off to the Nearest Integer)


$\mathrm{T}_{\mathrm{a}}=2 \pi \sqrt{\frac{\mathrm{M}}{\mathrm{K}}}$

$\mathrm{T}_{\mathrm{b}}=2 \pi \sqrt{\frac{\mathrm{M}}{\mathrm{K} / 2}}$


$\Rightarrow \mathrm{x}=2$


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