### Vibration of Multi-Degrees-of-Freedom Systems

The JavaScript program of this page calculates *eigenfrequencies* and *mode shapes* of Multiple Degree of Freedom Systems.

The mode shapes are visualized. The free vibrations in each mode are simulated.

Masses here are points masses, they don't have mass moment of inertia.
Each point mass in the plane has 2 DoF (degrees of freedom). Therefore a system of n point masses has at maximum
2*n DoF.

Due to bearings and rigid links the system will loose a corresponding amount of DoFs.

The number of eigenvalues that can be calculated equals the number of degrees of freedom of the system analized.

In case the system has possibilities to move without spring deformation, there will be corresponding mode shapes with eigenfrequency 0.

The calculated eigenvectors have 2 components for each node:

u is the displacement in x-direction and

v is the displacement in y-direction.

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