Find the stiffness and mass matrices of the beam supported on springs as shown in Fig. 12.19. Model the beam using one finite element. Assume the material of the beam as steel with a Young's modulus of \(207 \mathrm{GPa}\) and weight density of \(7650 \mathrm{~N} / \mathrm{m}^{3}\). Neglect the weights of the springs.

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1000 N 3 Y 60 4' 60 7 5 X 1 1500 N 1 m + 1 m- FIGURE 12.18 Seven-member planar truss. 500 N 6 60 2