Consider two identical springs each of spring constant $k$ 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)
JEE MAIN 2021, Medium
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$T _{ a }=2 \pi \sqrt{\frac{ M }{ K }}$
$T _{ b }=2 \pi \sqrt{\frac{ M }{ K / 2}}$
$\frac{ T _{ b }}{ T _{ a }}=\sqrt{2}=\sqrt{ x }$
$\Rightarrow x =2$
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