What is the ratio between the distance travelled by the oscillator in one time period and amplitude?

Motion of oscillator can be divided into 4 parts,

At t=0, it is at its mean position

At t=T/4, it covers the maximum distance A

At t=T/2, it moves back to its mean position from maximum amplitude and covers a distance of A

At t=3T/4, it again moves to its maximum position and covers a distance of A

At t=T, it again moves back to its mean position and covers distance of A

∴ in one cycle it covers total of 4A distance

∴ ratio of the distance covered in once cycle to the amplitude

(Note: in this question we are asked to find the distance and not displacement ∴ we do not use S.H.M. equation , which gives displacement of the particle from its mean position)