Question

For the damped oscillator shown in Figure, the mass m of the block is 200 g, k = 90 Nm^–1 and the damping constant b is 40 gs^–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

Answer 1

(b) If T is the time, when amplitude drops to half value then amplitude of the damped oscillations at time t is 

(c) If T’ is the time, when mechanical energy drops to half its mechanical energy E₀ , then mechanical energy E of the damped oscillations at an instant t is given by