Determine the direct frequency-response function, \(\frac{X_{1}}{F_{1}}\), for the two degree of freedom system shown in Fig. P9.2 using receptance coupling. Express your final result as a function of \(m, c, k\), and the excitation frequency, \(\omega\). You may assume a harmonic forcing function, \(F_{1} e^{i \omega t}\), is applied to coordinate \(X_{1}\).

Fig. P9.2 Flexible damped coupling of mass (I) to spring-mass-damper (II) to form the two degree of freedom assembly III.

C II I W k m + X1 2m + x2 C C M k m W 2k 2m X III X2