Question

Assertion :The graph between velocity and displacement for a harmonic oscillator is an ellipse. Reason: Velocity does not change uniformly with displacement in harmonic motion.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

In simple harmonic oscillator the velocity is given by:
$v=\omega \sqrt{a^2-y^2}$
$v^2={\omega }^2{a}^2-{\omega }^2{y}^2$
Dividing both sides by ${\omega }^2{a}^2$
$\frac{v^2}{{\omega }^2{a}^2}+\frac{y^2}{a^2}=1$
This is an equation of ellipse.
Yes the velocity does not change uniformly with displacement in harmonic motion. But this is not the reason for ellipse shaped graph.