The velocity vector v and displacement vector x of a particle executing SHM are related as v dvdx=-ω2x with the initial condition v = v0 at x = 0. The velocity v when displacement is x, is
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a
v=v02+ω2x2
b
v=v02-ω2x2
c
v=v03+ω3x33
d
v=v0-ω3x3ex31/3
answer is B.
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Detailed Solution
Given, vdvdx=-ω2xOn integrating within the limit, ∫v0vvdv=∫0x-ω2xdx⇒ v22v0v=-ω2x220x⇒ v2-v02=-ω2x2⇒ v=v02-ω2x2