Question

In a damped oscillation with damping constant b. The time taken for its mechanical energy to drop to half. What is its value?

(A) (b/m) ℓn 2

(B) (b / 2m) ℓn 2

(C) (m/b) ℓn 2

(D) (2m / b) ℓn 2

Answer 1

The correct option is (C) (m/b) ℓn 2.

Explanation:

Mechanical energy = E = Eo e–(bt/m)

Given E = (Eo / 2). Let the time be T'

∴ (Eo / 2) = Eo e(–bT/m)

∴ (2)–1 = e–(bT/m)

∴ ℓn 2 = (bT / m) ℓn e

∴ T = (m/b) ℓn 2