1.

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

Answer»

`(1)/(8)`
`(1)/(6)`
`(2)/(3)`
`(1)/(9)`.

Solution :For damped oscillator `r=r_(0)e^(-gamma t)`
where r is damping factor.
Time for 100 OSCILLATIONS `=(100)/(v)`
`:.""(r_(0))/(3)=r_(0)e^(-gamma(100)/(v))""…(i)`
and `""r.=r_(0)e^(-gamma(100)/(v))""...(ii)`
DIVIDING (ii) by (i)
`:.""(3R.)/(r_(0))=(e^(-(200gamma)/(v)))/(e^(-(100gamma)/(v)))=e^(-(100gamma)/(v))`
`:.""r.=(1)/(3)r_(0)e^(-(100gamma)/(v))`
`r.=(1)/(3)r_(0)((1)/(3))""["Using eqn. (i)"]`
`:.""r.=(r_(0))/(9)`
Correct choice is (d).


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