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Mechanical Engineering QUESTION #2450
Question 1
For a 2-DOF undamped system with mass matrix \([M]\) and stiffness matrix \([K]\), the natural frequencies are found from:
  • Setting \(\det([K]-\omega^2[M])=0\) (the characteristic/frequency equation)✔️
  • Setting \(\det([M]+\omega^2[K])=0\)
  • Solving \([M]\{\ddot{x}\}=0\)
  • Setting \(\text{tr}([K])\cdot\omega=0\)
Correct Answer Explanation
For a multi-DOF undamped system, assuming harmonic solution and substituting yields \(([K]-\omega^2[M])\{X\}=\{0\}\). For non-trivial solution: \(\det([K]-\omega^2[M])=0\).