When a particle executes simple Harmonic motion, the nature of graph of velocity as function of displacement will be

Step-by-step solution

The displacement equation of a particle is given by x = A sin ω t + ϕ ⇒ sin ω t + ϕ = x A The velocity equation is given by, v = ω A cos ω t + ϕ ⇒ cos ω t + ϕ = v ω A Since, sin 2 θ + cos 2 θ = 1 ⇒ x 2 A 2 + v 2 ω 2 A 2 = 1 The above equation represents an ellipse.