A mechanical system is depicted in the figure below. A pinion with fixed rotation axis passing through C2 meshes with a translatory rack of mass m = 0.8 kg. The rack, which is supported on two...

Extracted text: A mechanical system is depicted in the figure below. A pinion with fixed rotation axis passing through C2 meshes with a translatory rack of mass m = 0.8 kg. The rack, which is supported on two identical guides (bearings), each of damping coefficient c = 12 N s/m, meshes with another solid pinion that, as a result, rolls without slippage on another fixed rack. Derive the differential equation describing the movement of the system. Determine transfer function G(s) = X(s)/F(s) where X(s) is the Laplace transform of x(t) and F(s) is the Laplace transform of f(t). Find x(t) if the input is f(t) = 80(t) = step function. The system parameters are: J1 = 0.001 kg m² and J2 = 0.0003 kg m², m. = 0.4 kg, the radii R1 = 0.05 m, R2 = 0.07 m, R = 0.06 m, the stiffness k = 160 N/m, %3D a. b. C. Pinion J2 R Rack Guide RI Pinion R2 Fixed rack