Determine the response of the system in Problem 6.51 to the initial conditions \(x_{1}(0)=1\), \(\dot{x}_{1}(0)=0, x_{2}(0)=2, \dot{x}_{2}(0)=1, x_{3}(0)=1\), and \(\dot{x}_{3}(0)=-1\). Assume \(k / m=1\).

Data From Problem 6.51:-

Find the natural frequencies and mode shapes of the system shown in Fig. 6.6 (a) when \(k_{1}=k, k_{2}=2 k, k_{3}=3 k, m_{1}=m, m_{2}=2 m\), and \(m_{3}=3 m\). Plot the mode shapes.

Figure 6.6(a):-

Transcribed Image Text:

x1 k k 000 m a m2 x2 15 k3 m3