Velocity-Displacement Graph in SHM – Rankers Physics
Topic: Oscillation
Subtopic: Equation of SHM

Velocity-Displacement Graph in SHM

A particle is executing SHM. Then, the graph of velocity as a function of displacement is a/an:
straight line
circle
ellipse
hyperbola

Solution:

For a particle in SHM, velocity \(v = \omega \sqrt{A^2 - x^2}\). Squaring and rearranging gives \(\frac{v^2}{\omega^2 A^2} + \frac{x^2}{A^2} = 1\), which represents an ellipse.

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