Question: As shown in Figure, disk 1 is driven by an external moment M(t). Disk 2 is connected torsionally to disk 1 by a shaft and rolls without slipping on the cart.
The following system properties apply: I1 = 1.5 (105) kg mm2, D1 = 200 mm, L = 1250 mm, G = 79 GPa, d = 50 mm, I2 = 0.5 (103) kg mm2, D2 = 175 mm, M = 75 kg, kA = 2 kN/mm, and kB = 1.5 kN/mm.
Tasks: (a) Select coordinates and draw a free-body diagram for motion of the two disks and the cart.
(b) Obtain the EOM for each body.
(c) Present the coupled equations of motion in matrix format.
(d) Obtain the eigenvalues, natural frequencies, and normalized eigenvectors.
(e) State the uncoupled modal equations of motion and the transformation from modal to physical coordinates.