Oscillations

JEE Main level, single correct, medium

46 of 194

Question 46 of 194

When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is:

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Answer: (B) elliptical

For a particle executing SHM,
x=Asin⁡(ωt+ϕ)x=A\sin \left(\omega t+\phi \right)
v=ωAcos⁡(ωt+ϕ)v=\omega A\cos \left(\omega t+\phi \right)
⇒v2ω2A2+x2A2=1⇒\Rightarrow \dfrac{{v}^{2}}{{\omega }^{2}{A}^{2}}+\dfrac{{x}^{2}}{{A}^{2}}=1\Rightarrow equation of ellipse between vv and xx

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