A particle is performing harmonic motion if its velocity are `v_(1)` and `v_(2)` at the displecement from the mean position are `y_(1)` and `y_(2)` respectively then its time period is

Explanation

`v_(1) =omega sqrt(A^(2) -y_(1)^(2)), v_(2) = omega sqrt(A^(2)-y_(2)^(2))` to find amplitude
`(v_(1)^(2))/(v_(2)^(2))=(A^(2)-y_(1)^(2))/(A^(2)-y_(2)^(2))rArrA =sqrt((v_(1)^(2)y_(2)^(2)-v_(2)^(2)y_(1)^(2))/(v_(1)^(2)-v_(2)^(2)))` to find time period
`V_(1)^(2) - v_(2)^(2) = omega^(2) (y_(2)^(2) -y_(1)^(2)) rArr T = 2pi sqrt((y_(2)^(2)-y_(1)^(2))/(v_(1)^(2)-v_(2)^(2)))`