The amplitude of a damped oscillator becomes half in one minutes. The amplitude after 3 minutes will be 1/x times of the original . Determine the value of x.

Options

A. `2 xx 3`
B. `2^(3)`
C. `3^(2)`
D. `3 xx 2^(2)`

Answer

B

Explanation

Amplitude of damped oscillator
`A(t) = A_(0) e^(-((b)/(2m))t)`
`(b)/( 2 m) ` = constant
For t = 1 min ` (A_(0))/( 2) = A_(0) e^((-bt)/(2m)) rArr e^((-b)/(2m)) = (1)/(2) rArr e^((-b)/(2m)) = 2 `
For t = 3 min, ` A = A_(0) e^(-((b)/(2m))xx3) = (A_(0))/( ( e^(+b// 2m))^(3))`
`rArr A = (A_(0))/( 2^(3)) :. X = 2 ^(3)`