2. A support for electrified railway cables is cantilevered from the side of the track by a beam with spring stiffness k. The mass of the beam is 3M and is assumed to be concentrated at the free end. The cable, of mass 2M, is supported by a spring of stiffness k from the end of the cantilever. The system of equations governing the motion of the system is: 3 M y_{1}^{\prime \prime}=-2 k y_{1}+k y_{2} 2 M \ddot{y}_{2}=k y_{1}-k y_{2} k = 22 Write the above system of differential equations in matrix form. Then, by considering the trial solution: y = e"X, show that system can be written as an eigenvalue problem. (3) b) Find the general solution for the system of equations by solving the eigenvalue problem. (12)

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2. A support for electrified railway cables is cantilevered from the side of the track by a beam with spring stiffness k. The mass of the beam is 3M and is assumed to be concentrated at the free end. The cable, of mass 2M, is supported by a spring of stiffness k from the end of the cantilever. The system of equation