Oscillations Part 1

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.