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Question

A particle executes S.H.M., the graph of velocity as a function of displacement is:


A

a circle

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B

a parabola

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C

an ellipse

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D

a helix

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Solution

The correct option is C

an ellipse


Explanation for the correct option(s):

C: An eclipse

For a body performing SHM, the relation between velocity and displacement

v=ω(A2x2)

Now, square both the sides

v2=ω2(A2x2)v2=ω2A2ω2x2v2+ω2x2=ω2A2

Divide the whole equation by ω2A2

v2/ω2A2+ω2x2/ω2A2=ω2A2/ω2A2v2/(ωA)2+x2/(A)2=1

The above equation is similar to the standard equation of an ellipse, so the graph between velocity and displacement will be an ellipse.

Hence, option C is correct.


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