Question

The equation of motion of ad amped harmonic oscillator is given by
d 2 x + 2 b d x + ω 02 x = 0 dt2 dt
with m = 0.25kg, b = 0.14s−1 and ω0 =18.4s−1.
Calculate i) the time period; ii) number of oscillations in which its amplitude will become half of its initial value; and iii) number of oscillations in which its mechanical energy will reduce to half of its initial value.