Final answer:
The time taken by a particle to complete 5/8 of an oscillation in simple harmonic motion is 5/8 of the period T, which is 0.625 × T or 5T/8. While none of the provided options (a.T/12, b.T/6, c.5T/12, d.7T/1) precisely match this value, it appears there might be a typographical error in the options. The student should be requested to verify the options for accuracy.
Step-by-step explanation:
The subject of the question is simple harmonic motion (SHM), specifically regarding the calculation of the time taken by a particle to complete a portion of an oscillation. In SHM, the time period, denoted as T, is the time it takes for one complete cycle. If we need to calculate the time taken to complete 5/8 of an oscillation, we multiply the fraction of the oscillation (5/8) by the period T.
Now, to determine the exact answer:
- Time for one oscillation (T): Time period of the motion.
- Time taken for 5/8 oscillations: 5/8 × T
Performing the calculation yields:
(5/8) × T = 0.625 × T = 5T/8
Since none of the provided options exactly match 5T/8, all the options are wrong. However, it seems that there could be a typo in the last option, 7T/1, which might incorrectly express the fraction 7/8 or another intended value. Without the correct options, we would have to request clarification on the given options.
Please note, as an SHM question, it is critical to pay attention to the exactness of the given options to solve these types of problems effectively. The information given in the problem statement and the available choices should align to provide an accurate answer.
Therefore, without the correct options, or assuming a typo in the options provided, the question as it stands does not have a satisfactory answer from the given choices. The student should be encouraged to double-check the options provided in the question.