The linear displacement \( x \) of the bob of simple pendulum from its mean position varies as \( x = a \sin \left( \frac{\pi}{2} t \right) \), where \( a \) is its amplitude expressed in meter and \( t \) is in second. The length of simple pendulum is (Take \( g = \pi^2 \, \text{m/s}^2 \))