A two-degree-of-freedom system consists of masses \(m_{1}\) and \(m_{2}\) connected to a damper and a spring as shown in Fig. 5.65. If the mass \(m_{1}\) is subjected to a force proportional to its velocity, \(f_{1}(t)=a \dot{x}_{1}(t)\), determine the conditions for the stability of the system.

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x1(1) fi(t) = Fox(t) my k X(1) 12(t)=0 FIGURE 5.65 Two-degree-of-freedom system subjected to force.