Question: In Figure, the shaft ends that support gears 1 and 2 are rigidly attached to ground. The gears are rigidly engaged. The shaft for gear 1 has a 20 cm length, a 5 cm diameter, and a 95 GPa shear modulus. Gear 1 has a 15 cm radius and a 1.5 kg m2 mass moment of inertia. The shaft for gear 2 has a 10 cm length, a 7.5 cm diameter, and a 85 GPa shear modulus. Gear 2 has a 22.5 cm radius and a 1.75 kg m2 mass moment of inertia. The pulley attached to gear 2 has a radius of 10 cm. The weight attached to the cable from the pulley has a mass of 10 kg, and the cable has a stiffness
of 90 N/mm. The pulley attached to gear 2 has negligible mass. Neglect torsional drag at the bearings. Tasks:
(a) Select coordinates and draw free-body diagrams for each mass/inertia element.
(b) Apply the kinematic constraint to eliminate an unneeded coordinate. Separately state the independent equations of motion and then put them in matrix format.
(c) For the properties given, determine the natural frequencies