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

1. straight line passing through origin
2. circle
3. hyperbola
4. ellipse

Correct answer: ellipse

Solution

The momentum of the particle is given by p = mv = mωa cos(ωt). Since x = a sin(ωt), the relationship between p and x is parametric, with x = a sin(ωt) and p = mωa cos(ωt). Eliminating t gives the equation of an ellipse: (x/a)^2 + (p/mωa)^2 = 1.

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