A particle of mass m oscillates along x-axis according to the equation x = a sin(ωt). 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 the equation x = a sin(ωt). The nature of the graph between momentum and displacement of the particle is:

G1 Physics · Accepted Answer

Step 1: Displacement x = a sin(ωt), velocity v = aω cos(ωt), and momentum p = maω cos(ωt). Step 2: Divide by their maximum values: x/a = sin(ωt) and p/(maω) = cos(ωt). Step 3: Eliminate time: x²/a² + p²/(m²a²ω²) = 1. Step 4: This is the equation of an ellipse in the p–x plane. Final answer: (C) ellipse.