Figure 3.1 shows a simple representation of a load-leveling system. This might be a truck suspension where a load change represented by the disturbance force Fa will change the height of the structure mass and we desire the structure mass to return to its original position. On trucks, this control is most often done using pneumatic devices, but here we simply postulate a controllable velocity source V. AFd Ms AV'S bs Vc Min = 0 Figure 3.1: A load-leveling system(b) Based on the bond graph with causality, choose the state variables as the momentum variable p, of the mass my, the displacement variable q, of the spring ks and the displacement x of the mass m, . Please derive the state equations and put them into the standard matrix representation x = Ax + BV. + BaFa- (c) Apply Laplace transform to matrix representation x = Ax + BcVc + BaFa and derive the transfer functions X Ve (s) and Fa (s). (d) Derive the complex frequency response functions X V (s). Plot the variation of the magnitude of frequency response with different damping by (from zero to some value) and frequency values