Question

The un-damped system has angular frequency w=15Hz.The system is then damped withdamping constant y=5Hz.at what angular frequency must the system be driven in order to achieve the maximum amplitude ?

Answer 1

$w_d = w \sqrt{1-ξ^2} \\ = \sqrt{w^2-(ξw)^2} \\ = \sqrt{w^2- γ^2} \\ = \sqrt{15^2-5^2} \\ = \sqrt{200} \\ = 14.14 \;Hz$