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)