The force \((F)\)-deflection \((x)\) relationship of a nonlinear spring is given by

\[F=a x+b x^{3}\]

where \(a\) and \(b\) are constants. Find the equivalent linear spring constant when the deflection is \(0.01 \mathrm{~m}\) with \(a=20,000 \mathrm{~N} / \mathrm{m}\) and \(b=40 \times 10^{6} \mathrm{~N} / \mathrm{m}^{3}\).