a
$F_{1}=m \omega^{2} x$
$T=\frac{2 \pi}{\omega}$
$F=m a=4 m \pi^{2} x \frac{1}{T^{2}}$
$\therefore F_{1}=\frac{4 m \pi^{2}}{T_{1}^{2}} x$
$F_{2}=\frac{4 m \pi^{2}}{T_{2}^{2}} x$
$F_{1}+F_{2}=\frac{4 m \pi^{2} x}{T^{2}}+\frac{4 m \pi^{2} x}{T_{2}^{2}}$
$\frac{1}{T^{2}}=\frac{1}{T_{1}^{2}}+\frac{1}{T_{2}^{2}}$
$\therefore T=\frac{12}{25}$