A single-story building frame is modeled by a rigid floor of mass \(m\) and columns of stiffness \(k\), as shown in Fig. 3.58. It is proposed that a damper shown in the figure is attached to absorb vibrations due to a horizontal ground motion \(y(t)=Y \cos \omega t\). Derive an expression for the damping constant of the damper that absorbs maximum power.

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-x(t) 22 m K2 y(t) Y cos wot FIGURE 3.58 Damped single story building subjected to ground acceleration.