d
$\mathrm{T}_{1}=2 \pi \sqrt{\frac{\mathrm{m}}{\mathrm{k}_{1}}} \quad$ or $\mathrm{k}_{1}=\frac{4 \pi^{2} \mathrm{m}}{\mathrm{T}_{1}^{2}}$
${\mathrm{T}_{2}=2 \pi \sqrt{\frac{\mathrm{m}}{\mathrm{k}_{2}}}} {\text { or } \quad \mathrm{k}_{2}=\frac{4 \pi^{2} \mathrm{m}}{\mathrm{T}_{2}^{2}}}$
${\mathrm{Now} \quad \mathrm{T}=2 \pi \sqrt{\frac{\mathrm{m}}{\mathrm{k}_{2}}}} {\text { or } \quad \mathrm{k}=\frac{4 \pi^{2} \mathrm{m}}{\mathrm{T}_{2}^{2}}}$
In parallel $\mathrm{k}=\mathrm{k}_{1}+\mathrm{k}_{2}$
Substituting the values of $\mathrm{k}, \mathrm{k}_{1}$ and $\mathrm{k}_{2}$ we get:
$\frac{1}{\mathrm{T}^{2}}=\frac{1}{\mathrm{T}_{1}^{2}}+\frac{1}{\mathrm{T}_{2}^{2}}$