Determine the response of the system of Figure P6.4 and Chapter Problems 6.4 and 6.13 if the right-hand disk is given an angular displacement of \(2^{\circ}\) clockwise from equilibrium and the left-hand disk is given an angular displacement of \(2^{\circ}\) counterclockwise.

Data From Chapter Problem 6.4:

Derive the differential equations governing the two degree-of-freedom system shown in Figure P6.4 using \(\theta_{1}\) and \(\theta_{2}\) as generalized coordinates.

Data From Chapter Problem 6.13:
Determine the natural frequencies of the system of Figure P 6.4 if \(I_{1}=0.3 \mathrm{~kg} \cdot \mathrm{m}^{2}\), \(I_{2}=0.4 \mathrm{~kg} \cdot \mathrm{m}^{2}, J_{1}=J_{2}=1.6 \times 10^{-8} \mathrm{~m}^{4}, G_{1}=G_{2}=80 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}\), and \(L=30 \mathrm{~cm}\). Determine the modal fractions for each mode. Identify any nodes.

Transcribed Image Text:

J, G J2, G2 3L L FIGURE P6.4