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.

Explanation

Amplitude of damped oscillations is `A=A_(0)e^(-gammat)`
`" "`(from `x=x_(m)e^(-gammat)`)
As `A=A_(0)//2 " at " t=1` minute,
So `(A_(0))/(2)=A_(0)e^(-gamma) " or "e^(gamma)=2`
After 3minutes the amplitude will be `A_(0)//x`
So `(A_(0))/(x)=A_(0)e^(-gamma3)`
or `x=e^(3y)=(e^(gamma))^(3)=2^(3)=8`