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The amplitude of velocity of a particle acted on by a force F=cos ω t along the x direction, is given by x=1aω2-bω+c where a,b,c, are constants and b2<4 ac. . For what value of ω does the resonance occur?

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a

ω=b2a

b

ω=ba

c

ω=c

d

ω=0

answer is A.

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Detailed Solution

X=1aω2−bω+c At resonance X becomes maximum and aω2−bω+c becomes minimum. ∴ Differentiate above term and equating it to zero. ∴2aω−b=0⇒ω=b2a

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The amplitude of velocity of a particle acted on by a force F=cos ω t along the x direction, is given by x=1aω2-bω+c where a,b,c, are constants and b2<4 ac. . For what value of ω does the resonance occur?