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Q.

A graph of the square of the velocity against the square of the acceleration of a given simple harmonic motion is

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a

b

c

d

answer is D.

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Detailed Solution

x=Asin⁡ωt v=dxdt=Aωcos⁡ωt=ωA2−x2a=dvdt=−Aω2sin⁡ωt=dvdt=−ω2x But  x=−aω2∴ v=ωA2−a2ω4  or  v2=ω2A2−a2ω4
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A graph of the square of the velocity against the square of the acceleration of a given simple harmonic motion is