Final answer:
The period of the simple harmonic motion described by the equation d=4 sin(8π t) is 0.25 seconds.
Step-by-step explanation:
To determine the period of a simple harmonic motion for the equation d = 4 sin(8π t), we need to look at the coefficient of t in the sine function, which is 8π. This coefficient is related to the angular frequency of the motion, ω, which is defined as ω = 2π/period (T). Since the angular frequency ω is given as 8π, we can write the relationship as 8π = 2π/T. Solving this for the period (T), we get T = 2π/8π, which simplifies to T = 1/4 seconds. Therefore, the period of this simple harmonic motion is 0.25 seconds.
It's important to note that the period of a simple harmonic motion represents the time it takes for the oscillating particle or body to complete one full cycle of motion.