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Simple Harmonic Motion — JEE physics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceJEE physicsSimple Harmonic Motion1 Mark
Question
Assertion : The graph between velocity and displacement for a harmonic oscillator is a parabola.
Reason : Velocity does not change uniformly with displacement in harmonic motion.
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Answer

(e) $\ln \mathrm{SHM}, v=\omega \sqrt{a^2-y^2}$ or $v^2=\omega^2 a^2-\omega^2 y^2$.Dividing both sides by $\omega^2 a^2, \frac{v^2}{\omega^2 a^2}+\frac{y^2}{a^2}=1$. This is the equation of an ellipse. Hence the graph between $v$ and $y$ is an ellipse not a parabola.

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