For the three-cart system illustrated in Figure 2, obtain the equations of motion. The system has three inputs u(t), u2(t), and us(t) and three outputs x1(t), 2(t), and r3(t). Obtain three second-order differential equations with constant coefficients. Write the equations of motion in matrix form. Once the system has been represented in matrix form, find the transfer function X1(s)/U3(s) for U2(s) = U3(8) = 0. (30 pts.) = 112 k₁ k₂ kz M₁ www M₂ wwwy M3 b₁ 00 b₂ OO by Figure 2: Three-cart system with three inputs and three outputs. This figure has been extracted of [1]