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Compare LC oscillations and a force damped oscillations in mechanics.

Answer»

Solution :The equation of forced damped oscillations is,
`(d^(2)x)/( dt^(2)) + ( b)/( m ) ( DX)/( dx) + ( K )/( m ) x= (F_(0) )/( m)cos omegat`and equation of LCoscillation,
`(d^(2)q)/( dt^(2))+( R )/( L ) (dq)/( dt)+ = ( V_(m))/( L ) sin omega t `
`{:("Forced oscillations","Driven LCR circuit"),(m(d^(2)x)/(dt^(2))+b(dx)/(dt) kx = F cos omega_(d)t,L(d^(2)q)/(dt^(2)) + R (dq)/( dt) + (q)/(C ) = V_(m) sin omega t ),("Displacement x ","Charge on capacitor q"),("Time t","Time t"),("Mass m","SELF inductance L"),("Damping constant b","Resistance R"),("Spring constant K","Inverse capacitance "1//C),("Driving frequency" omega_(d),"Driving frequency " omega),("Natural frequency of oscillations"omega,"Natural frequency of LCR circuit " omega_(0)),("AMPLITUDE of forced oscillations A","Maximum charge stored "q_(m)),("Amplitude of driving force "F_(0),"Amplitude of applied voltage"v_(m)):}`


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