A particle startsits SHM at `t=0` . At a particular instant on its way to extreme position , `x= (A)/(2)` . Find the time taken by the particle to come back to this point after passing through the extreme position.
Hint `: t_(1) = ` time taken to go from `x=0` to `x= (A)/(2)`
`t_(2) =` time taken to go to extreme position and come back to mean position `= (T)/(2)`
Required time `= (T)/(2) - t_(1)`

Explanation

`t_(1)=`time taken to go from `y=0` to `y= (A)/(2)` is`(T)/(12)` (Refer solution)
`t_(2) =` time taken to go from mean `rarr` extreme `rarr`mean position
`= (T)/(2)`
Required time `=t_(2 )-t_(1) = (T)/(2) - (T)/(12) = (5T)/(12)`