Final answer:
The period for the simple harmonic motion equation d = 4 sin(8πt) is ½ second, based on the relationship between period and angular frequency.
Step-by-step explanation:
For the simple harmonic motion equation d = 4 sin(8πt), the period of the motion can be determined by looking at the coefficient of t inside the sine function. In the equation given, the coefficient is 8π, which represents the angular frequency ω. The period T is related to the angular frequency by the formula T = 2π/ω. Therefore, the period of the motion described by the equation is T = ½ second, which corresponds to choice B. 0.5.