When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is :

Solution

Physics sir · 4 steps

Write v in terms of x, square both sides, and the curve tells you its own shape.

1. Velocity formula. For SHM with amplitude A and angular frequency ω, the velocity at displacement x is v = ±ω√(A² - x²).
2. Square and rearrange. Squaring gives v² = ω² (A² - x²). Divide both sides by ω² A² and bring the x term across.

   x²/A² + v²/(ω² A²) = 1

3. Read the shape. This is the standard form of an ellipse with semi-axes A along x and ω A along v. It would look like a circle only if the two semi-axes happened to be equal on the graph, which is not true in general.
4. So. The velocity versus displacement graph is elliptical, which is option (d).

The idea to keep. In SHM, v against x is an ellipse, because x² and v² add up to a constant. Remember that a against x is a straight line through the origin.

Answer from the NTA final answer key. Solution by PrepWiser.