A massless bar of length \(1 \mathrm{~m}\) is pivoted at one end and subjected to a force \(F\) at the other end. Two translational dampers, with damping constants \(c_{1}=10 \mathrm{~N}-\mathrm{s} / \mathrm{m}\) and \(c_{2}=15 \mathrm{~N}-\mathrm{s} / \mathrm{m}\) are connected to the bar as shown in Fig. 1.109. Determine the equivalent damping constant, \(c_{\mathrm{eq}}\), of the system so that the force \(F\) at point \(A\) can be expressed as \(F=c_{\mathrm{eq}} v\), where \(v\) is the linear velocity of point \(A\).

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0.25 m == C = 15 N-s/m F 0.75 m C = 10 N-s/m 0.25 m FIGURE 1.109 Rigid bar connected by dampers.