When a particle executes Simple Hormonic Motion, the nature of graph of velocity as a function of displacement will be :

Solution

Physics sir · 3 steps

Eliminate time between x and v, and the equation that drops out is an ellipse.

1. Write x and v. Take x = A sin ω t. Differentiating gives v = Aω cos ω t.
2. Remove time. Use sin² ω t + cos² ω t = 1, with sin ω t = x/A and cos ω t = v/(Aω).

   x²/A² + v²/A²ω² = 1

3. So. This is an ellipse with semi-axes A along x and Aω along v. The answer is (b).

The idea to keep. A graph of one quantity against another, with no time axis, needs time eliminated. In SHM, v against x and a against v both give ellipses, while a against x is a straight line.

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