A simple harmonic oscillator has an amplitude $A$ and time period $6 \pi$ second. Assuming the oscillation starts from its mean position, the time required by it to travel from $x = A$ to $x = \frac { \sqrt { 3 } } { 2 } A$ will be $\frac { \pi } { x } \mathrm {~s}$, where $x =$ $\_\_\_\_$ .