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. 8
B. 2
C. 3
D. 4

Answer

A

Explanation

The variation in amplitude of damped harmonic oscilator with time is given by
`A=A_(0)e^(-bt)`
`A_(0)`=Initial amplitude, b=damping factor
It is given that after 1 minute, `A_(1)=A_(0)//2=A_(0)e^(-bt)`
`:. 2=e^(b)`
`:.` after 3 minutes, `A_(3)=A_(0)//x=A_(0)e^(-3b)`
`:. x=2^(3)`