The amplitude of a damped oscillator becomes half in one minute. The amplitude after three minutes will be `(1)/(x)` times the original, then find the value of x.

Options

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

Answer

B

Explanation

Amplitude of damped oscillation at time t,
`A(t) = A_(0)e^(-(bt)/(2m))`
After `t= 1 min, A(2) = (A_0)/(2)`
`therefore (A_0)/(2) = A_(0)e^(-(b(1))/(2m))`
`therefore (1)/(2)= e^(-(b)/(2m))`
`therefore 2 = e^(-(b)/(2m))" ""........."(1)`
Now, after `t= 3 min, A(3) = (A_0)/(x)`
`therefore (A_0)/(x) = A_(0)e^(-(b(3))/(2m))`
`therefore (1)/(x)= e^(-(3b)/(2m))`
`therefore x = e^((3b)/(2m))= (e^((b)/(2m)))^(3)`
`therefore x= 2^(3)` (from equation (1)).