Correct Answer - B
Here string becomes slack when acceleration of body becomes more than g above equilibrium position. Hence during that period, `SHM` disappears:
upto `P_(3), SHM` appears and between `P_(3) & P_(4), SHM` disapears. `= (2T_(1))/(3) +(t_(P_(3)P_(4))+t_(P_(4)P_(3))):`
`:. T = t_(OP_(2))+t_(P_(2)O) +t_(OP_(3))+t_(P_(3)P_(4)) +t_(P_(4)P_(3)) +t_(P_(3)O)`
where: `T_(1) = 2pi sqrt((,)/(k))` velocity at `P_(3)` is:
`v = omega sqrt(A^(2)-x^(2)) = omega sqrt(4b^(2)-b^(2)) = b omega sqrt(3)`
`t_(P_(3)P_(4)) +t_(P_(4)P_(3)) = (2v)/(g)`