The force ((F))-velocity ((dot{x})) relationship of a nonlinear damper is given by [F=a dot{x}+b dot{x}^{2}] where (a)
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The force \((F)\)-velocity \((\dot{x})\) relationship of a nonlinear damper is given by
\[F=a \dot{x}+b \dot{x}^{2}\]
where \(a\) and \(b\) are constants. Find the equivalent linear damping constant when the relative velocity is \(5 \mathrm{~m} / \mathrm{s}\) with \(a=5 \mathrm{~N}-\mathrm{s} / \mathrm{m}\) and \(b=0.2 \mathrm{~N}-\mathrm{s}^{2} / \mathrm{m}^{2}\).
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