1. A gearbox is modeled as which comprises two identical gears of moments of inertia J1 and N1 teeth, meshing with two identical pinions of moments of inertia J2 and N2 teeth. All three shafts have stiffness k. For the relations given below:

find the natural frequencies and natural modes of the system. Sketch the latter.

2. Derive a procedure to obtain the zero-state response of a two-dof semidefinite system that does not preserve the generalized—translational or angular— momentum. To this end, use as an example the belt-pulley system.