(a) Find the roots of the frequency equation of the system shown in Fig. 5.5 with the following data: \(m_{1}=m_{2}=50 \mathrm{~kg}, k_{1}=k_{2}=3500 \mathrm{~N} / \mathrm{m}, k_{3}=0, c_{1}=c_{2}=c_{3}=0\).

(b) If the initial conditions are \(x_{1}(0)=x_{2}(0)=5 \mathrm{~cm}, \dot{x}_{1}(0)=\dot{x}_{2}(0)=0\), determine the displacements \(x_{1}(t)\) and \(x_{2}(t)\) of the masses.

Figure 5.5:-

Transcribed Image Text:

k m fi(t) -x(t) k kx1 m1 Spring k under tension for +1 (a) -X1,X1 K(x2-x1) 12(12-11) Spring k under tension for+(x2-x1) (b) -x2(1) -2(t) k3 00000 m2 C3 -X2, X2 -2 K3x2 m2 -C312 Spring k3 under compression for +x FIGURE 5.5 A two-degree-of-freedom spring-mass-damper system.