A particle starts from wave motion and has a time period T. If it completes 5/8 oscillations time taken is?

Total distance covered by the particle=4A.

 

we divide this whole path in 8 intervals of A/2.

 

so, 5/8 oscillations means, it has already completed1/2 oscillation(i.e. total dist. = 2A) and is half way to the other side i.e. A/2.

 

so,A/2=Asinwt,w=2pi/T ,

 

substitute to get t=T/12.

 

now, total time taken = time to complete previous one half(2A) + time taken to completeA/2=t/2+t/12=7T/12.

 

Hence option B is correct

Starting from mean position, time taken by it to complete 5/8 oscillations, is. Total distance covered by the particle=4A. we divide this whole path in 8 intervals of A/2. so, 5/8 oscillations means, it has already completed1/2 oscillation