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 oscillation
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 .