Finding natural frequency and mode shape of damped 4 degree of freedom

Assume that the m1= 40 kg, m2 = 1800 kg, I = 5000 kg-m2, l1 = 3.2 m, l2= 2.1 m, k1 = k2 = 90,000 N/m, and c = 800 Nm/s;

1. Determine natural frequencies and the mode shapes.
2. Considering the base displacement x1(t) = 0.1 sin (66t) applied on the right side only.

Answer 1

[J Chen]

Use F=ma to develop the differntial equations for m1, m2. Use F=ma and M=Iw for m3. The natural frequencies and mode shapes are the eigenvalues and eigenvectors.