The amplitude of a damped oscillator becomes half in one minute. The amplitude after 3 munutes will be `(1)/(x)` times the original . Then , x is

Options

A. 4
B. 8
C. 6
D. 12

Answer

B

Explanation

Amplitude of damped oscillator,
`A = A_(0)e^(-lambdat)`
Where , `lambda` = constant , t = time
for , t = 1 min
`(A_(0))/(2) = A_(0)e^(-lambda)rArr e^(lambda) = 2`
for, t = 3 min
`A = A_(0) (e^(-lambda))^(3)`
`rArr (A_(0))/((e^(lambda))^(3))=(A_(0))/(2^(2)) rArr X = 2 ^(3) = 8 " "[:. (A_(0))/(2^(3)) = (A_(0))/(X)]`