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  4. When a particle executes simple Harmonic motion, the nature of graph of velocity as function of displacement will be :

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Q. When a particle executes simple Harmonic motion, the nature of graph of velocity as function of displacement will be :

JEE MainJEE Main 2022Oscillations

Solution:

For a particle in SHM, its speed depends on position as
$v =\omega \sqrt{ A ^2- x ^2}$
Where $\omega$ is angular frequency and $A$ is amplitude
Now $v^2=\omega^2 A^2-\omega^2 x^2$
So, $\frac{v^2}{(\omega A )^2}+\frac{x^2}{( A )^2}=1$
So graph between $v$ and $x$ is elliptical