In dampled oscillations, the amplitude of oscillatinos is reduced to one-fourth of its initial value 10cm at the end of 50 oscillations. What will be its amplitude when the oscillator completes 150 oscillations ?

Explanation

As`a=a_(0)e^(-bt//2m)`, let T be the time period of oscillation
Case (I),`(a_(0))/(4)=a_(0)e^(-bxx50T//2m)`
or `(1)/(4)=e^(-50bT//2m` …(i)
Case (II), `a=a_(0)e^(-bxx150T//2m)`
`=a_(0)(e^(-50bT//2m))^(3)=a_(0)((1)/(4))^(3)`
`=10((1)/(64))cm=0.156cm`