GATE Mechanical Engineering (ME) 2022 Shift 2 Solved Paper

For a dynamical system governed by the equation,
$\ddot{\mathit{x}}\left(\mathit{t}\right)+2\mathit{\zeta }{\mathit{\omega }}_{\mathit{n}}\dot{\mathit{x}}\left(\mathit{t}\right)+{\mathit{\omega }}_{\mathit{n}}^2\mathit{x}\left(\mathit{t}\right)=0$
the damping ratio ζ is equal to $\frac{1}{2\mathit{\pi }}{\log }_{\mathit{e}}2$. 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).