For a dynamical system governed by the equation,

mẍ(t) + 2ζω_nẋ(t) + ω_n²x(t) = 0,

the damping ratio ζ is equal to (1 / 2π) 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).