\(M{\omega ^2}x = \left[ {\rho Ag + k} \right]x\)

\( \Rightarrow \omega  = {\left[ {\frac{{\rho Ag + k}}{m}} \right]^{1/2}}\)

\( \Rightarrow T=2\pi {\left[ {\frac{M}{{\left( {k + A\sigma g} \right)}}} \right]^{1/2}}\)

It Should be less than \(2\pi {\left[ {\frac{M}{{\left( {k + A\sigma g} \right)}}} \right]^{1/2}}\)