Answer :
The damping ratio for the system is 0.94.
A damping effect is one that reduces or stops oscillation in an oscillatory system by affecting it internally or externally. The damping ratio is a dimensionless statistic indicating how oscillations in a system diminish after a disturbance. In physical systems, damping is produced by processes that dissipate the energy contained in the oscillation.
The formula is :
[tex]w_{d}[/tex] = [tex]w_{n}[/tex][tex]\sqrt{1-c^{2} }[/tex]
where, in plugging the values gives:
[tex]3[/tex] = [tex]9[/tex] [tex]\sqrt{1-c^{2} }[/tex]
c = 0.94
Therefore, the system's damping ratio is 0.94.
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