If the amplitude of velocity of a particle acted on by a force F = F0 cos ωtalong x-axis is given by:


Find the condition of resonance and resonant frequency. 


Correct option is

b2 = 4ac


At resonance  will be max → ∞.   

i.e., resonance frequency ω = (b/2a)                     …(2)

further substituting the value of ω from eqn. (2) in (1), we get


Which is the required condition of resonance

Alternative solution:-

At resonance 

Now as at resonance ω is single valued, which is possible only if


Which is the required condition of resonance, and so at resonance ω = (b/2a) [substituting b2 = 4ac in Eqn. (1)].



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