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.

Explanation

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)`