The slender bar of Figure 3.9(a) has a mass of 31 kg and a length of 2.6 m. A 50 N force is statically applied to the bar at P then removed. The ensuing oscillations of Pare moni- tored, and the acceleration data is shown in Figure 3.9(b) where the time scale is calibrated but the acceleration scale is not. (a) Use the data to find the spring stiffness k and the damping cocfficient c.

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Consider the following hydraulic / mechanical system, where pi and P2 are the inputs to the system, and the piston is driving a pendulum. Assuming small angles 0 and a concentrated mass ma distance L1 from the pivot. Pell (P2 R2 P1 Pa ¡P3 R1 P4 L2 Li Develop the dynamic equation to model of the piston displacement, 0, as a function of the inputs, p1 and p2 in standard form. b. If you were to consider the input to the system to be the difference between the pressure on 0(s) either side of the piston, write the transfer function for the displacement of the piston: AP(s) Xj = 0 c. Develop the state equations for this system if the state variables are: