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In dampled oscillations, the amplitude o...

In dampled oscillations, the amplitude of oscillation is reduced to one-third of its initial value of `9cm` at the end of `100` oscillations. What will be its amplitude of oscillation in `cm` when it completes `200` oscillations.

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The correct Answer is:
1
Here, `a_(0)=9cm.`
Case I. `a=(a_(0))/(3)=(9)/(3)=3cm, `when`t=100T`,
where `T` is the time period of oscillation. ltbr. Case II. When `t=200,a=?`
For damped oscillations, `a=a_(0)e^(-bt//2m)`
Case I. `3=9e^(-bxx10bT//2m`
or `(1)/(3)=e^(-bxx100T//2m)` ...(i)
Case II. `a=9e^(-b 200T//2m)=9(e^(-bT//2m))^(2)`
`=9((1)/(3))^(2)=1cm`
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