solve the prob 2.5 with values as ?1 = ?1, ?2 = ?1? , ?3 = ?2, ?4 = ??2, ?1 = ?2, ?2 = ?1 textbook:- CONTROL SYSTEM DESIGN An Introduction to State-Space Methods BERNARD FRIEDLAND 

N 22 M 00 M Figure P2.4 Spring-coupled masses (two-car train). Problem 2.5 Two-car train An idealized two-car train consists of a pair of masses coupled by a spring, as shown in Fig. P2.4. The wheels of each car are independently driven by an electric motor such as described in Example 2B. (Also see Prob 2.1.) (a) Express the differential equations of the system in state-space form. (Find the A and B matrices.) Assume R is the motor resistance, K is the spring constant, k is the motor torque constant, and r = 7/f is the ratio of the motor torque to the linear force applied to the car. Use the following state and control variables x = Z x = Z2 where e, and e are the voltages on the drive motors. (b) Draw the block diagram of the system. u = e 2 = e2