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If for damped oscillations if (k)/(m) = ...

If for damped oscillations if `(k)/(m) = ((b)/(2m))^(2)`, then is the oscillation exist?

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No, because angular frequency fo damped oscillator is
`omega.= sqrt((k)/(m)-(b^2)/((2m)^2))" if "(k)/(m)= ((b)/(2m))^(2)" then "omega.=0`
Periodic time will be infinite.
Oscillation does not exist.
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