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

Question

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

Infinity Learn · Accepted Answer

$$x=asin$$ωt or $$xa=$$$$sin$$ωt        ......(i)  Velocity, $$v=dxdt=a$$ω$$cos$$ωt vaω$$=$$$$cos$$ωt                            ......(ii)  Squaring and adding (i) and (ii), we get  $$x2a2+v2a2$$ω$$2=sin2$$ω$$t+cos2$$ωt $$x2a2+v2a2$$ω$$2=1$$  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.

A particle of mass m oscillates along x -axis according to equation $x = a \sin ω t$ . The nature of the graph between momentum and displacement of the particle is

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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

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A particle of mass m oscillates along x -axis according to equation $x = a \sin ω t$ . The nature of the graph between momentum and displacement of the particle is