In damped oscillatory motion a block of mass `20kg` is suspended to a spring of force constant `90N//m` in a medium and damping constant is `40g//s`. Find (a) time period of oscillation (b) time taken for amplitude of oscillation to drop to half of its intial value (c) time taken for its mechanical energy to drop to half of its initial value.

For the damped oscillator shown in Fig. 14.19, the mass m of the block is 200 g, k = 90 N m^(-1) and the damping constant b is 40 g s^(-1) . Calculate (a) the period of oscillation, (b) time taken for its amplitude of vibrations to drop to half of its initial value, and (c) the time taken for its mechanical energy to drop to half its initial value.