Harmonic Oscillator Graph – Rankers Physics

Equation of SHM: Practice Problem & Solution

Assertion (A): The graph between velocity and displacement for a harmonic oscillator is a parabola. Reason (R): Velocity does change uniformly with displacement in harmonic motion.  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Equation of SHM. Understanding the underlying formula is key to arriving at the correct answer below:

For a harmonic oscillator, velocity \( v \) and displacement \( x \) are related by \( v = \omega \sqrt{A^2 - x^2} \). Squaring this gives \( v^2 = \omega^2 (A^2 - x^2) \), which is an equation of an ellipse, not a parabola. So (A) is false. Velocity does not change uniformly with displacement, hence (R) is also false. Thus, both A and R are false.

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