Since, the particle is executing SHM. Therefore, displacement equation of wave will be y=Asinωt ⇒y∕A=sinωt and wave velocity equation will be vy=
dy
dt
=Aωcosωt ⇒vy∕Aω=cosωt Now, sin2ωt+cos2ωt=1 ∴(y∕A)2+(vy∕Aω)2=1 This equation is similar to the equation of ellipse.