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When an oscillator completes 100 oscillations its amplitude reduced to 1/3 of initial value. What will be its amplitude, when it completes 200 oscillations?

Answer»

`1//8`
`2//3`
`1//6`
`1//9`

Solution :This is a case of damped vibratin as the AMPLITUDE of vibration is decreasing with TIME.
Now, when `t= 100 T, a=a_(0)//3`[T is time period]
Let the amplitude be a at t= 200 T i.E, after completing 200 oscillations.
`therefore a =a_(0)//3 = a_(0)e^(-100Th)`............ (i)
and `a. = a_(0)e^(-200 Th)`........(ii)
From (i) `1/3 = e^(-100Th), therefore e^(-200 Tb) = 1//9`
From (ii), `a. = a_(0) xx 1/9 =a_(0)/9`
`therefore` The amplitude will be reduced to 1/9 of initial value.


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