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 .

Options

A. 1.25
B. 2.5
C. 5
D. 3.75

Answer

A

Explanation

For damped oscillator `A = A_(0)e^(-bt)`
`(A_(0))/(2) = A_(0) e^(-bx (25T)/(2m))(or) (1)/(2) = e^(-25 (bT)/(2m))`
`A = A_(0) e^(-bx 50 (T)/(2m)) = A_(0) (e^(-25 (bT)/(2m)))^(2)`