Question: As shown in Figure, the cylinder of mass M and radius R rolls without slipping on the plane and is attached to the cart of mass m by spring kB. Spring kA connects the cart to ground and spring kC connects the cylinder to ground. The following data set applies: M = 25 kg, R = 50 mm, m = 10 kg, kA = 1000 N/m, kB = 2500 N/m, kC = 1000 N/m.
Tasks:
(a) Select coordinates and draw free-body diagrams for each body.
(b) Obtain the EOM for each body. Present the equations in matrix format.
(c) For the given properties, obtain the eigenvalues, normalized eigenvectors, and natural frequencies of the system.
(d) State the uncoupled modal equations of motion and the transformation from modal to physical coordinates.
