Explain about eigen values for free vibration ?

Question

Accepted Answer

Eigen values for free vibration represent the natural frequencies at which a system will vibrate without any external forces.

Eigen values are the values of natural frequencies at which a system vibrates without any external forces.
They are obtained by solving the characteristic equation of the system.
Each eigen value corresponds to a mode shape, which describes the pattern of vibration.
Higher eigen values indicate higher natural frequencies and shorter periods of vibration.
Eigen values are important in analyzing the dynamic behavior of structures and systems.
For example, in a vibrating guitar string, the eigen values represent the frequencies at which the string will naturally vibrate when plucked.

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