Consider the mechanical dynamic system in Figure 2.40 where the movement of a large object is controlled by manipulating a much smaller object that is mechanically coupled with it. A force \(u(t)\) is applied to the small mass \(\mathbf{m}\) in order to position the larger mass \(\mathbf{M}\). The coupling between the objects is modelled by a spring constant \(\mathbf{k}\) with a damping coefficient \(\mathbf{b}\). Find the State-Variable Matrix model of the system.

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U m Figure 2.40 Mass, spring and damper system. b M -000 k