The amplitude of a damped oscillator becomes half in one minute. The amplitude after 3 minutes will be 1 x times the original. Then x is

Step-by-step solution

In damped oscillation, amplitude changes according to following formula- a = a 0 e - b t Here a 0 = Initial amplitude a = Amplitude at any time t Using given data- a 0 2 = a 0 e - b × 1             … 1 and   a 0 x = a 0 e - b × 3       … 2 From equation 1 - ⇒     e - b = 1 2 Using equation 1   and   2 - ⇒     x 2 = e - b e - 3 b = e - b e - b 3 ⇒     x 2 = 1 2 1 2 3 = 4 ⇒   &#