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Determine frequency ratios

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In the idealized model shown (See Attached)
m = slug, k = 9 lb/ft and the viscous damping factor is 0.15. For what range of frequency ratios will the magnification be greater than 1?

(please see attached for details)

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Please see attached file

For M > 1, we want (1-r2)2 + 4zeta2r2 < 1

Or zeta = ...

Solution Summary

The expert determines the frequency ratios. The range of frequency ratios that the magnification will be greater than one is discussed.