Seen in Figure 1, a small cart (with mass m and position x2) is riding inside a larger cart, which is massless, and has a position 1. A spring and a damper in parallel connect the larger cart to the smaller cart, and another spring connects the exterior of the large massless cart to an input position, xu. For this problem, the diagram is similar to the one in Homework 2, Problem 1. It has the same equations of motion. You are not required to re-derive the equations of motion - please reference the solutions. Given this, Xu x1 X2 Ctiven equation of motion: Small cart: m x 2 + ((x2-x)+ K(1-x)=0 large corr: Klx2-2x1+x ) + C(x-x)=0 Ca k k www m C Your tasks: Figure 1: Schematic of the mechanical system to model in Problem 1. A. Find the state-space equations for the system in matrix form using x and x2 and their derivatives. B. Represent the mechanical system in 2nd order matrix form using 1 and 2 and their derivatives.