Equation we get before `v = v_(max)sqrt(1- x^2/A^2)` Side view of circular motion is simple harmonic motion. `=>` `v_(max) = (2πA)/T` `=>` (1) `T = 2πA/v_(max)` From energy conservation, we have `1/2 kA^2 = 1/2mv_(max)^2` `=>` `A/v_(max)^2 = sqrt(m/k)` substitute into equation (1) `=>`