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The forced harmonic oscillations have equal displacement amplitude at frequencies `omega_(1)=400 s^(-1)` and `omega_(2)=600 s^(-1)`. Find the resonance frequency at which the displacement amplitude is maximum. |
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Answer» Since `a=(F_(0)//m)/(sqrt((omega^(2)-omega_(0)^(2)+2 beta^(2))^(2)+ 4 beta^(2)( omega_(0)^(2)- beta^(2))))` we must have `omega_(1)^(2)-omega_(0)^(2)+2 beta^(2)=-( omega_(2)^(2)-omega_(0)^(2)+ 2 beta ^(2))` or ` omega_(0)^(2)-2 beta^(2) =( omega_(1)^(2)+ omega_(2)^(2))/( 2) = omega_(res)^(2)` |
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