The force-velocity relationship of a nonlinear damper is given by \(F=500 v+100 v^{2}+50 v^{3}\), where \(F\) is in newton and \(v\) is in meters/second. Find the linearized damping constant of the damper at an operating velocity of \(5 \mathrm{~m} / \mathrm{s}\). If the resulting linearized damping constant is used at an operating velocity of \(10 \mathrm{~m} / \mathrm{s}\), determine the error involved.