The amplitude of a damped oscillation becomes half in 1minute. If the amplitude after 4minute will be 1y times of the original, find the value of y.
A
4
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B
8
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C
16
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D
32
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Solution
The correct option is C16 We know that amplitude of damped oscillation varies exponentially and given as, A=Aoe−rt....(1) where r=b2m As A=Ao2 at t=1minute ⇒Ao2=Aoe−r ⇒e−r=12 Or, e+r=(e−r)−1=2....(2) After 4minute the amplitude will be Aoy, putting t=4minute in Eq.(1) Aoy=Aoe−4r y=e4r=(er)4 Substituting from Eq.(2), ⇒y=(2)4=16