A small \(3.0-\mathrm{kg}\) object dropped from the roof of a tall building acquires a terminal speed of \(25 \mathrm{~m} / \mathrm{s}\). Assume the drag force exerted on the object has the same form as the damping force exerted on a damped oscillator; that is, the force is opposed to the motion, and its magnitude is linearly proportional to the object's speed. An object identical to the dropped one is attached to a vertical spring ( \(k=230 \mathrm{~N} / \mathrm{m})\) and set into oscillation in the air with an initial amplitude of \(0.20 \mathrm{~m}\).

(a) What is the quality factor for this oscillation? 

\((b)\) How long does it take for the amplitude to drop to half its initial value?

(c) How much energy is lost in this time interval?