In simple harmonic motion, starting from rest, At t=0,x=A x=A‌cos‌ω‌t‌‌...(i) When t=τ,x=A−a When t=2τ,x=A−3a From equation (i) A−a=A‌cos‌ω‌τ‌‌...(ii) A−3a=A‌cos‌2‌ω‌τ‌‌...(iii) As cos‌2‌ω‌τ=2cos2ωτ−1...(iv) From equation (ii),(iii) and (iv) ‌