Two carts with negligible rolling friction are connected as shown in Figure 2. An input force u(t) is applied.The masses of the two carts are M, and M, and their

displacements are x(t) and q(t), respectively. The carts are connected by a spring k and a damper b. Answer the following questions: By using Newton's Second Law, derive two mathematical equations that describe the motion of thetwo carts. (5 marks)(a) (b)According to your ß value, answer one of the following two questions (10 marks): 0 \leq \beta \leq 13: \text { Determine the transfer function } G_{1}(s)=\frac{Q(s)}{U(s)} 14 \leq \beta \leq 18: \text { Determine the transfer function } G_{2}(s)=\frac{X(s)}{U(s)}