Derive the equations of motion for the free vibration of the system shown in Fig. 5.53. Assuming the solution as \(x_{i}(t)=C_{i} e^{s t}, i=1,2\), express the characteristic equation in the form

\[a_{0} s^{4}+a_{1} s^{3}+a_{2} s^{2}+a_{3} s+a_{4}=0\]

Discuss the nature of possible solutions, \(x_{1}(t)\) and \(x_{2}(t)\).

Transcribed Image Text:

ell mi k k x(1) ell m2 x2(1) ell k3 FIGURE 5.53 Damped two-degree-of-freedom system.