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1. Consider the following one-input two-output system: p k2 k m Cart m Cart M, M. b2 b, u(t), the force on M1, is the input to the system, and p(t) and q(t) the speeds of M1 and M2, respectively, are the system outputs. Determine a state space description for the system. [50 Points] 2. Consider a dc motor an electro-mechanical system with an electrical input and mechanical output: B E be Vis the input (voltage) to the motor and Tis the output (torque). The torque T on the mechanical side is proportional to the current on the electrical side. The back emf E on the electrica side is proportional to the angular speed รจ on the mechanical side. Determine a state space description for the system. [30 Points] 3. Consider the following single-input single-output linear time invariant system: Ic(t) l(t) R 1(t) is the system input and Ic(t) its output. Determine a state space description for the system. [20 Points]

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