(b) $2\pi \sqrt {\frac{m}{k}} = 0.6$ …$(i)$ and $2\pi \sqrt {\frac{{m + m'}}{k}} = 0.7$ …$(ii)$

Dividing $(ii)$ by $(i)$ we get ${\left( {\frac{7}{6}} \right)^2} = \frac{{m + m'}}{m} = \frac{{49}}{{36}}$

$\frac{{m + m'}}{m} – 1 = \frac{{49}}{{36}} – 1 \Rightarrow \frac{{m'}}{m} = \frac{{13}}{{36}}$ $⇒$ $m' = \frac{{13m}}{{36}}$

Also $\frac{k}{m} = \frac{{4{\pi ^2}}}{{{{(0.6)}^2}}}$

Desired extension$ = \frac{{m'g}}{k}$

$ = \frac{{13}}{{36}} \times \frac{{mg}}{k}$$ = \frac{{13}}{{36}} \times 10 \times \frac{{0.36}}{{4{\pi ^2}}} \approx 3.5\;cm$