In Figure P11.33 the input u is an acceleration provided by the control system and applied in the horizontal direction to the lower and of the rod. The horizontal displacement of the lower and is y. The linearized from of Newton's law for small angles gives

a. Put this model into state variable form by letting x1 = ( and x2 = .
b. Construct a state variable feedback controller by letting u = k1x1 + k2 x2. Over what ranges of values of k1 and k2 will the controller stabilize the system? What does this formulation imply about the displacement y?
Figure P11.33

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Itt 71