A mass is suspended separately by two different springs in successive order then time period is $t_1$ and $t_2$ respectively. If it is connected by both spring as shown in figure then time period is $t_0$, the correct relation is :

Question

( A ) $t_0^2=t_1^2+t_2^2$
( B ) $t_0=t_1+t_2$
( C ) $t_0^{-1}=t_1^{-1}+t_2^{-1}$
( D ) $t_2^{-2}=t_1^{-2}+t_2^{-2}$