A particle undergoes s.h.m having time period T. The time taken by it to complete 3 / 8th, oscillation starting from mean position
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To find the time taken by a particle to complete a fraction of its oscillations starting from the mean position in Simple Harmonic Motion (SHM), we need to use the equation for the time period.
The time period (T) of an object undergoing SHM is defined as the time taken by the particle to complete one full oscillation or one complete cycle. In other words, it is the time taken to move from one extreme point to another and back to the same point again.
Let's denote the fractional part of oscillations we want to calculate as 'f' (in this case, 3/8).
The time taken to complete 'f' fraction of oscillations starting from the mean position can be calculated using the formula:
Time taken (t) = f * T
Where,
t = Time taken to complete 'f' fraction of oscillations
f = Fractional part of oscillations (3/8 in this case)
T = Time period of the particle's SHM
So, to find the time taken by the particle to complete 3/8th of an oscillation starting from the mean position, you would multiply the time period (T) by the fraction (3/8):
t = (3/8) * T
Note: Make sure the time period (T) is in the appropriate units (e.g., seconds) for accurate calculations.