Final answer:
The amplitude of a particle undergoing Simple Harmonic Motion (SHM) cannot be determined solely from the distances traveled in the first two seconds while starting from rest. More information would be required to establish a direct relationship between these distances and the amplitude. The correct answer is 'none of these'.
Step-by-step explanation:
The question is related to the concept of Simple Harmonic Motion (SHM), specifically concerning the amplitude of the oscillation. In SHM, a particle's acceleration is directly proportional to its displacement from the mean position and is always directed towards the mean position. Given that a particle travels a distance 'a' in the first second from rest, and a distance 'b' in the next second, we can utilize the properties of SHM to find the amplitude. The distances 'a' and 'b' are not sufficient to determine the amplitude directly due to the non-linear nature of SHM, but given the information about the time intervals and the distances, these can suggest something about the position of the particle relative to the amplitude at different time intervals.
If we consider these intervals from the equilibrium position (mean position), it could be that the particle starts from the equilibrium position, moves towards the amplitude, and then returns partway back towards equilibrium. However, it's mentioned that the particle covers both distances 'a' and 'b' on the same side of the mean position, which gives us important information about the particle's motion. Unfortunately, without more information or a specific relationship to use, this problem does not provide a clear solution, which implies the amplitude cannot be determined from the given data alone, and none of the provided options (a, b, c) appear to be derived from a valid equation relating to these distances and SHM.
Therefore, the correct answer to the question of finding the amplitude based on the provided details is option (d) none of these.