A particle execute shm in linear horizontal direction with time period t while starts its motion from one of the extreme position then find out the time taken by the particle in compete 7/8 oscillation

To determine the time taken by a particle executing simple harmonic motion (SHM) to complete 7/8 of an oscillation, we first need to understand the relationship between the time period of the motion and the fraction of the oscillation completed.

Understanding the Time Period

The time period (T) of an oscillating particle is the time it takes to complete one full cycle of motion. In this case, since the particle starts from one of the extreme positions, it will take half of the time period to reach the equilibrium position and then another half to return to the opposite extreme. Thus, the total time for one complete oscillation is T.

Calculating Time for 7/8 of an Oscillation

To find the time taken for 7/8 of an oscillation, we can use the following steps:

• Since one complete oscillation takes time T, the time for 1/8 of an oscillation can be calculated as:
• Time for 1/8 oscillation = T/8
• Therefore, the time for 7/8 of an oscillation can be expressed as:

Time for 7/8 oscillation = Time for 1 complete oscillation - Time for 1/8 oscillation

Mathematically, this can be represented as:

Time for 7/8 oscillation = T - (T/8) = (8T/8) - (T/8) = (7T/8)

Final Calculation

Thus, the time taken by the particle to complete 7/8 of an oscillation is:

Time taken = (7/8) * T

In summary, if you know the time period T of the oscillation, you can easily find the time taken for 7/8 of the oscillation by multiplying T by 7/8. This relationship is fundamental in understanding the dynamics of simple harmonic motion.