Obtain state-spacc representations of the mechanical systems shown in Figures 15?36(21) and (b). For the spring?mass-pullcy system of Figure 5-37.1hc moment of inertia of the pulley about the axis of rotation isJ and the radius is R. Assume that the system is initially in equilibrium. The gravitational force of mass m causes a static deflection of the spring such that k8 = mg. Assuming that the displacement y of mass m is measured from the ?cquilibl?ium position, obtain a state-spacc representation of the system. The external force u applied to mass m is the input and the displacement y is the output of the system.

State-Space Approach to Modeling Dynamic Systems

Figure 5-36 (a) and (b) Mechanical systems.

Figure 5-37 Spring-mass-pulley system.

www k m O 77 k ww (a) m x (Output) u(t) (Input force) x (Output) 777. u(t) (Input force) y U m mg R 777 0 mm 8