Test Index

Oscillations Part 1

Section: Physics

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Question : 27 of 100

Marks: +1, -0

A particle executes SHM, the graph of velocity as a function of displacement is

[26 Feb 2021 Shift 2]

a circle
a parabola
an ellipse
a helix

Solution:

Velocity of particle in

\text{SHM}

in terms of displacement

x

is given as

v \; = \omega \sqrt{A^{2} - x^{2}}

\Rightarrow

v \; = A \omega \sqrt{1 - \frac{x^{2}}{A^{2}}}

\Rightarrow

\frac{v}{A \omega} \; = \sqrt{1 - \frac{x^{2}}{A^{2}}}

\Rightarrow

\frac{v^{2}}{A^{2} \omega^{2}} \; = 1 - \frac{x^{2}}{A^{2}}

\Rightarrow

\frac{v^{2}}{A^{2} \omega^{2}} +

\frac{x^{2}}{A^{2}} \; = 1

. . . (i)

As equation of ellipse is

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

Eq. (i) is similar to the equation of ellipse. So, the graph between velocity and displacement is an ellipse.

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