Consider the system in Figure P4.6.

Figure P4.6 

a. Derive the differential equations of motion and obtain mass, stiffness, and damping matrices.

b. Assume that \(m=11 \mathrm{~kg}, k=4,511 \mathrm{~N} / \mathrm{m}\), and \(c=20 \mathrm{~N}-\mathrm{sec} / \mathrm{m}\). Determine the damping ratio and the undamped natural frequency for each mode.

c. Obtain and plot response when \(x_{1}(0)=0.01 \mathrm{~m}, \dot{x}_{1}(0)=1 \mathrm{~m} / \mathrm{sec}\), \(x_{2}(0)=-0.02 \mathrm{~m}\), and \(\dot{x}_{2}(0)=0\).

Transcribed Image Text:

Massless and rigid bar C x2 2m 3m k 2k