A viscous damper, with damping constant \(c\), and a spring, with spring stiffness \(k\), are connected to a massless bar \(A B\) as shown in Fig. 2.109. The bar \(A B\) is displaced by a distance of

\(x=0.1 \mathrm{~m}\) when a constant force \(F=500 \mathrm{~N}\) is applied. The applied force \(F\) is then abruptly released from its displaced position. If the displacement of the bar \(A B\) is reduced from its initial value of \(0.1 \mathrm{~m}\) at \(t=0\) to \(0.01 \mathrm{~m}\) at \(t=10 \mathrm{~s}\), find the values of \(c\) and \(k\).

C -0000000000 k B F= 500 N FIGURE 2.109 Spring-damper system subjected to force.