Time to Complete 3/8 Oscillation in Simple Harmonic Motion
To find the time taken for a particle undergoing simple harmonic motion to complete 3/8 of an oscillation, we need to first understand the relationship between time period and number of oscillations.

Time Period (T) and Number of Oscillations
- The time period (T) of a particle undergoing simple harmonic motion is the time taken to complete one full oscillation.
- The number of oscillations completed in a given time interval is directly proportional to the time interval and inversely proportional to the time period.
- Mathematically, the number of oscillations (n) completed in time interval (t) can be calculated using the formula: n = t/T

Calculating Time for 3/8 Oscillation
- To find the time taken for 3/8 of an oscillation, we can use the formula: t = n(T/8) where n = 3 (as we need to complete 3/8 oscillation).
- Substituting the values, we get: t = 3(T/8) = 3T/8

Final Calculation
- Therefore, the time taken for the particle to complete 3/8 of an oscillation is 3T/8.
- This means that the particle will take 3/8 of the time period (T) to complete the specified fraction of the oscillation.
By understanding the relationship between time period and number of oscillations, we can easily calculate the time taken for a particle in simple harmonic motion to complete a specified fraction of an oscillation.