Serway & Jewett — Oscillatory Motion: Problem 40

Consider the damped oscillator illustrated in Figure 15.19. The mass of the object is $375\text{ g}$, the spring constant is $100\text{ N/m}$, and $b = 0.100\text{ N} \cdot \text{s/m}$. (a) Over what time interval does the amplitude drop to half its initial value? (b) What If? Over what time interval does the mechanical energy drop to half its initial value? (c) Show that, in general, the fractional rate at which the amplitude decreases in a damped harmonic oscillator is one-half the fractional rate at which the mechanical energy decreases.