Simple Harmonic Motion

In figure \((\mathrm{A})\), mass '\(2 \mathrm{~m}^{\text {' }}\) is fixed on mass '\(\mathrm{m}\) ' which is attached to two springs of spring constant \(\mathrm{k}\). In figure (B), mass '\(\mathrm{m}\)' is attached to two springs of spring constant '\(\mathrm{k}\)' and '\(2 \mathrm{k}^{\prime}\). If mass '\(\mathrm{m}\)' in (A) and in (B) are displaced by distance '\(x^{\prime}\) horizontally and then released, then time period \(\mathrm{T}_{1}\) and \(\mathrm{T}_{2}\) corresponding to \((\mathrm{A})\) and (B) respectively follow the relation.