Question

The amplitude of a damped oscillator becomes half in one minute. The amplitude after 3 minutes will be `1/"X"` times the original, where X is ______. 

Options

• 2 × 3

• 2³

• 3²

• 3 × 2²

Answer 1

The amplitude of a damped oscillator becomes half in one minute. The amplitude after 3 minutes will be `1/"X"` times the original, where X is 2³ 

Explanation:

The amplitude of the damped oscillator is, A = A₀e^−λt

Fort =1 min, `"A"_0/2` = A₀e^−λt or e^λ = 2 

and for t = 3 min A = A₀ e^−λ×3

= `"A"_0/("e"^λ )^3 = "A"_0/2^3`

∴ x = 2³