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written 5.4 years ago by |
It is defined as the ratio of actual damping co-efficient to the critical damping coefficient.
i.e. $\xi = \frac{c}{c_c}$
Hence $\xi = \frac{c}{2mw_n}$
$\therefore$ $\xi w_n = \frac{c}{2m}$
Then the roots of characteristics equation can be written as
$s_1 = (\xi w_n) + \sqrt{ (\xi w_n)^2 - w^2_n}$
$= [ …