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(Solved): 2. The mass matrix and the stiffness matrix of a two DOF system are \( \mathbf{M}=\left[\b ...
2. The mass matrix and the stiffness matrix of a two DOF system are \( \mathbf{M}=\left[\begin{array}{ll}5 m & 2 m \\ 2 m & 5 m\end{array}\right] \) and \( \mathbf{K}=\left[\begin{array}{cc}20 k & 0 \\ 0 & 20 k\end{array}\right] \) respectively. (1) Determine the natural frequencies (5 pts). (2) Determine the mode shapes ( 3 pts). (3) Determine the modal matrix (1 pt). (4) Draw the diagram illustrating the mode shape vectors \( (1 \mathrm{pt}) \).
Expert Answer
Answer= (2)To determine the natural frequencies, we need to solve the eigenvalue problem Kx = lambdaM*x, where lambda is the eigenvalue and x is the c