Short Exercise 1:
Compute the natural frequencies and natural modes of the 3-degree of freedom system shown
below. Follow the following steps
1- Formulate the stiffness matrix. Use k as a prefactor.
2- Formulate the mass matrix. Use m as a prefactor.
3- Solve the eigenvalue problem assuming the natural frequencies can be written as
4- Compute the modal masses and modal stiffnesses. Would these values depend on the way
you normalize the eigenmodes.
5- Verify that the first Eigenmode is orthogonal to the second eigenmode.
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