In dampled oscillation , the amplitude of oscillation is reduced to half of its initial value of 5 cm at the end of 25 osciallations. What will be its amplitude when the oscillator completes 50 oscillations ?
Hint `: A= A_(0) e^((-bt)/(2m))` , let T be the time period of oxcillation
Case -I `: (A_(0))/(2) = A_(0)e^(-bx(25T)/(2m))`
or `(1)/(2)= e^(-25(bT)/(2m))` ......(i)
Case -II` A=A_(0)e^(-bxx50(T)/(2m))`
`A _(0)(e^(-25(bT)/(2m)))^(2)`
Use euation (i) to find a .

Explanation

`A = A_(0) e^(-bt //2m)`
Let T be the time period of osciallations
Case -I ` : (A_(0))/(2) =A_(0)e^(-25bT //2m)`
`(1)/(2) = e^(-25 bT //2m)` .....(i)
Case -II`: A = A_(0)e^(-50 bT //2m) = A_(0)( e^(-25bT//2m))^(2)`
`=A_(0)((1)/(2))^(2) ` using equation (1)
`=(5)/(4) cm = 1.25 cm`