Final answer:
The distance traveled by a particle of the string during one cycle of simple harmonic motion is 4A cm, where A is the amplitude of oscillation.
Step-by-step explanation:
The distance a particle of the string travels during one cycle of simple harmonic motion is based on the total movement from the maximum amplitude on one side, back to the maximum amplitude on the opposite side, and then back to the starting position. Since the amplitude A represents the maximum displacement of the particle from the equilibrium position, the particle would travel a distance of 2A to the opposite extreme, and then another 2A back to the start, totalling 4A centimeters for a complete cycle. It is essential to note that this distance is not the same as the wavelength of the wave. If we assume that the amplitude is given in centimeters, then the particle moves 4A cm during one cycle.