Final answer:
The maximum displacement from the equilibrium position in the simple harmonic motion equation 4sin(8πt) is the amplitude, which is 4.
Step-by-step explanation:
For the simple harmonic motion equation 4sin(8πt), the maximum displacement from the equilibrium position is represented by the amplitude of the sine function. The equilibrium position is the point where the object would stay at rest if there were no net forces acting on it, and it is also the central position around which the object oscillates.
The equation for simple harmonic motion given is 4sin(8πt). In this equation, the maximum displacement from the equilibrium position can be found by looking at the coefficient of the sine function, which is 4. So, the maximum displacement is 4.
In the given equation, the coefficient in front of the sine function (which is 4 in this case) determines the amplitude. Therefore, the maximum displacement from the equilibrium position is the amplitude, which is 4. This corresponds to option a. 4.