Question

The amplitude of a damped oscillator becomes half in one minute. The amplitude after 3 minutes will be 1/x time the original, where x is ………

(a) 2 × 3
(b) 2³
(c) 3²
(d) 3 × 2²

Answer 1

The amplitude of a damped oscillator that halves every minute will be 1/8 of the original amplitude after 3 minutes, indicating that option (b) 2³ is correct.

Step-by-step explanation:

The question relates to the exponential decay of the amplitude of a damped oscillator. If the amplitude becomes half in one minute, then after each minute, the amplitude is multiplied by another factor of 1/2, meaning that the amplitude decays by a factor of 1/2 over the course of each minute.

After 3 minutes, the amplitude will have decayed by a factor of (1/2) multiplied by itself 3 times. The decay rate is then (1/2)3, which is 1/8. Therefore, the amplitude after 3 minutes will be 1/8 of the original amplitude.

The answer is option (b) 23, meaning the amplitude will be 1/x of the original amplitude where x is 23 or 8.