Consider two identical springs each of spring constant k

Question:

Consider two identical springs each of spring constant $\mathrm{k}$ and negligible mass compared to the mass $\mathrm{M}$ 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)

Solution:

(2)

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

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

$\frac{\mathrm{T}_{\mathrm{b}}}{\mathrm{T}_{\mathrm{a}}}=\sqrt{2}=\sqrt{\mathrm{x}}$

$\Rightarrow \mathrm{x}=2$

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