The maximum permissible recoil distance of a gun is specified as \(0.5 \mathrm{~m}\). If the initial recoil velocity is to be between \(8 \mathrm{~m} / \mathrm{s}\) and \(10 \mathrm{~m} / \mathrm{s}\), find the mass of the gun and the spring stiffness of the recoil mechanism. Assume that a critically damped dashpot is used in the recoil mechanism and the mass of the gun has to be at least \(500 \mathrm{~kg}\).