A weight of \(25 \mathrm{~N}\) is suspended from a spring that has a stiffness of \(1000 \mathrm{~N} / \mathrm{m}\). The weight vibrates in the vertical direction under a constant damping force. When the weight is initially pulled downward a distance of \(10 \mathrm{~cm}\) from its static equilibrium position and released, it comes to rest after exactly two complete cycles. Find the magnitude of the damping force.