Chapter 12, Problem 66P

Consider the damped oscillator illustrated in Figure 12.16a. The mass of the object is 375 g, the spring constant is 100 N/m, and b = 0.100 N · 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.