For a dynamical system governed by the equation,

$\ddot{x}(t)+2\zeta {\omega }_n\dot{x}(t)+{\omega }_n^{2}x(t)=0$

the damping ratio ζ is equal to $\frac{1}{2\pi }{\log }_{e}2$. The displacement x of this system is measured during a hammer test. A displacement peak in the positive displacement direction is measured to be 4 mm. Neglecting higher powers (> 1) of the damping ratio, the displacement at the next peak in the positive direction will be _______ mm (in integer).