Answer to Question #66522 in Physics for raj jadhavar

Question

For a damped harmonic oscillator, the equation of motion is m (d 2 x / dt 2 ) + γ(dx / dt ) + kx = 0

with m = 0.50 kg, γ = 0.70 kgs−1 and k = 70 Nm−1. Calculate (i) the period of motion,
(ii) number of oscillations in which its amplitude will become half of its initial value,

(iii) the number of oscillations in which its mechanical energy will drop to half of its

initial value, (iv) its relaxation time, and (v) quality factor.