A simple pendulum has time period $T_1$. The point of suspension is now moved upward according to the relation $y=K{t}^2$, ($K=1 m/s^2$) where $y$ is the vertical displacement. The time period now becomes $T_2$. The ratio of $\frac{{T_1}^2}{{T_2}^2}$ is $\frac{\alpha }{\beta } \left[where, \alpha and \beta are co-prime\right].$ Find the value of $\left(2\beta \right).$  ($g=10m/s^2$)