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A particle is...

Question

A particle is executing linear simple harmonic motion about the origin x = 0. Which of the graphs shown in the figure represents the variation of the potential energy function U(x) versus displacement x?

A

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B

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C

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D

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Solution

The correct option is D

Here, $F = - k x \Rightarrow \frac{- d U}{d x} = - k x \Rightarrow \int_{0}^{U} d U = \int_{0}^{x} k x d x ∴ U = \frac{1}{2} k x^{2}$

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