d
As we know, time period, \(T=2 \pi \sqrt{\frac{\ell}{g}}\)

\( When\, additional \,mass \mathrm\,{M}\) is added then

\(\mathrm{T}_{\mathrm{M}}=2 \pi \sqrt{\frac{\ell+\Delta \ell}{\mathrm{g}}}\)

\(T_{\frac{M}{T}}=\sqrt{\frac{\ell+\Delta \ell}{\ell}}\) or \(\left(\frac{T_{M}}{T}\right)^{2}=\frac{\ell+\Delta \ell}{\ell}\)

or, \(\left(\frac{T_{M}}{T}\right)^{2}=1+\frac{M g}{A y}\left[\because \Delta \ell=\frac{M g \ell}{A y}\right]\)

\(\therefore \frac{1}{y}=\left[\left(\frac{T_{M}}{T}\right)^{2}-1\right] \frac{A}{M g}\)