A particle of mass m oscillates along x -axis according to equation x=asinωt. The nature of the graph between momentum and displacement of the particle is

x=asinωt or xa=sinωt        ......(i)  Velocity, v=dxdt=aωcosωt vaω=cosωt                            ......(ii)  Squaring and adding (i) and (ii), we get  x2a2+v2a2ω2=sin2ωt+cos2ωt x2a2+v2a2ω2=1  It is an equation of ellipse.   Hence, the graph between velocity and displacement is an ellipse.  Momentum of the particle =mv ∴ The nature of graph of the momentum and displacement  is same as that of velocity and displacement.