Question:
A particle executes S.H.M., the graph of velocity as a function of displacement is :
A particle executes S.H.M., the graph of velocity as a function of displacement is :
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In S.H.M., \(v^2 = \omega^2(A^2 - x^2)\), which is the equation of an ellipse in the v-x plane.
Updated On: Nov 4, 2026
- a parabola
- a helix
- an ellipse
- a circle
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The Correct Option is C
Solution and Explanation
For S.H.M., \(v = \omega\sqrt{A^2 - x^2}\), so \(v^2 = \omega^2 (A^2 - x^2)\).
Rearranging: \(\frac{x^2}{A^2} + \frac{v^2}{\omega^2 A^2} = 1\).
This is the standard equation of an ellipse with semi-axes A (along x) and \(\omega A\) (along v). It is a circle only if \(\omega = 1\), which is not general.
Answer: (3) an ellipse
Rearranging: \(\frac{x^2}{A^2} + \frac{v^2}{\omega^2 A^2} = 1\).
This is the standard equation of an ellipse with semi-axes A (along x) and \(\omega A\) (along v). It is a circle only if \(\omega = 1\), which is not general.
Answer: (3) an ellipse
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