Question

The graph between instantaneous velocity and displacement of a particle performing SHM is ______.

Options

• Parabola

• Straight line

• Ellipse

• Circle

Answer 1

The graph between instantaneous velocity and displacement of a particle performing SHM is Ellipse.

Explanation:

`v = ω sqrt(A^2 - x^2)`

v²= ω² (A² - x²)

v² = ω²A² − ω² x² 

v² + ω² x² = ω² A²

`v^2/ (ω^2A^2)+ (ω^2x^2)/(ω^2A^2 )= 1`

`v^2 /(ωA)^2 + x^2/(A)^2 = 1`

The above equation is similar to the equation of an ellipse

i.e `(y^2/a^2 + x^2/b^2 = 1).`

So, the graph between velocity and displacement will be an ellipse.