Explanation

(c) Under the influence of one force $F_{1} = m\omega_{1}^{2}y$ and under the action of another force, $F_{2} = m\omega_{2}^{2}y$
Under the action of both the forces $F = F_{1} + F_{2}$
$\Rightarrow m\omega^{2}y = m\omega_{1}^{2}y + m\omega_{2}^{2}y$
$\Rightarrow \omega^{2} = \omega_{1}^{2} + \omega_{2}^{2} \Rightarrow \left( \frac{2\pi}{T} \right)^{2} = \left( \frac{2\pi}{T_{1}} \right)^{2} + \left( \frac{2\pi}{T_{2}} \right)^{2}$
$\Rightarrow T = \sqrt{\frac{T_{1}^{2}T_{2}^{2}}{T_{1}^{2} + T_{2}^{2}}} = \sqrt{\frac{\left( \frac{4}{5} \right)^{2}\left( \frac{3}{5} \right)^{2}}{\left( \frac{4}{5} \right)^{2} + \left( \frac{3}{5} \right)^{2}}} = 0.48s$