c
(c) Under the influence of one force ${F_1} = m\omega _1^2y$ and under the action of another force, ${F_2} = m\omega _2^2y$.
Under the action of both the forces $F = {F_1} + {F_2}$
$ \Rightarrow m{\omega ^2}y = m\omega _1^2y + m{\omega ^2}y$
$ \Rightarrow \omega _1^2 + \omega _2^2$
$ \Rightarrow {\left( {\frac{{2\pi }}{T}} \right)^2} = {\left( {\frac{{2\pi }}{{{T_1}}}} \right)^2} + {\left( {\frac{{2\pi }}{{{T_2}}}} \right)^2}$
$ \Rightarrow T = \sqrt {\frac{{T_1^2T_2^2}}{{T_1^2 + T_2^2}}} $
$ = \sqrt {\frac{{{{\left( {\frac{4}{5}} \right)}^2}{{\left( {\frac{3}{5}} \right)}^2}}}{{{{\left( {\frac{4}{5}} \right)}^2} + {{\left( {\frac{3}{5}} \right)}^2}}}} = 0.48\,sec $