# Problem 12: Linear Analysis to Find the Complex Eigen Solution of a System

## Objective

The objective is to find the complex Eigen value solution for the system below.

## Entities Validated

- Rigid body
- Translational joint
- Force_Spring damper – translational

## Type of Analysis

- Linear

## Reference

Schaum’s Outline of, Theory and Problem of Mechanical Vibrations, First Edition by S Graham Kelly: 168 (ISBN 0-07-034041-2)

## Model Files

- complex_eigen_analysis_2DOF.mdl - MotionView Model
- complex_eigen_analysis_2DOF.xml - MotionSolve Deck

## Eigen File Results

## Result Comparison

Output | Analytical | MotionSolve | % Error |
---|---|---|---|

Mode 1, Real (Hz) | 0.2391 | 0.2391 | 0 % |

Mode 1, Imaginary (Hz) | 1.5775 | 1.5776 | 0.01 % |

Mode 2, Real (Hz) | 0.5566 | 0.5566 | 0 % |

Mode 2, Imaginary (Hz) | 2.6926 | 2.6927 | 0.004% |

## Conclusion

MotionSolve results compare well with analytical results.