[UPSC CSE 2025] Waves (Q2, 15M)

m \frac{d^2x}{dt^2} + \gamma \frac{dx}{dt} + kx = 0; A harmonic oscillator is represented by the equation m \frac{d^2x}{dt^2} + \gamma \frac{dx}{dt} + kx = 0; where m = 0\cdot 25\text{ kg}, \gamma = 0\cdot 07\text{ kg s}^{-1} and k = 85\text{ Nm}^{-1}. Determine (i) the period of oscillation, and (ii) the number of oscillations in which its amplitude will become half of its original value.