Question

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)

Answer 1

Answer: 2

$T_a=2\pi \sqrt{\frac{M}{K}}$
$T_b=2\pi \sqrt{\frac{M}{K/2}}$
$\frac{T_b}{T_a}=\sqrt{2}=\sqrt{x}$
$\Rightarrow x=2$