A particle performs SHM of time period T. Find the time taken by the particle to go directly (i) from its mea position to half the amplitude and (ii) from half the amplitude position to its positive extreme position.

A particle performs SHM of time period T. Find the time taken by the p

1.	A particle performs SHM of time period T. Find the time taken by the particle to go directly (i) from its mea position to half the amplitude and (ii) from half the amplitude position to its positive extreme position.
Answer» SOLUTION :When a particle is initially in the mean position. `X=A sin omega t` (i) When the particle travels from mean position to half its AMPLITUDE displacement`x=A//2` `A/2 =A sin omegat` `sin omega t=1/2 impliesomega t=(pi)/6implies(2pi)/T=t=(pi)/6impliest=T/12` (ii) The TIME taken to go from half the amplitude position to its positive extreme position =[Time taken to go from mean to positive extreme position ]-[Time taken to go from MENA to half amplitude position] `=T/4-T/12=T/6`