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